# Online Material

- Visa Vesterinen (VTT), Swinging up the quantum signal, QTF March meeting (2019):

- Matti Partanen (WMI), APS March meeting 2020 slides on “Quantum sensing and communication with superconducting microwave circuits”.
- The quantum internet is within reach (Technical University Munich Research News, 24.20.2019).
- An Introduction to Quantum Microwaves for Communication and Sensing (Frank Deppe is interviewed for AZoNano).
- Internet Quântica: mais rápida, segura e sensível, com protótipo em 2021. Portugal entrou nesta corrida através do Técnico, que ganhou dois projetos europeus de €13 milhões.

# Tutorials

- Tutorial on “Quantencomputing” given by Frank Deppe at the Academy for Teacher Training and Personnel Management in Dillingen a. d. Donau (2019-09-25).
- Tutorial on “Propagating Quantum Microwaves” given by Frank Deppe at the PhD School “Cryocourse 2018” at Aalto University.

# Papers

## 2020 |

Gonzalez-Raya, T; Sanz, M Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air Miscellaneous 2020. @misc{GonzalezRaya2020, title = {Coplanar Antenna Design for Microwave Entangled Signals Propagating in Open Air}, author = {T Gonzalez-Raya and M Sanz}, year = {2020}, date = {2020-09-01}, abstract = {Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a fridge, where they are created, into an environment dominated by thermal noise. Indeed, the states that carry such quantum resources are generated in a cryostat at $T_textin simeq 10^-2 $~K and with $Z_textin = 50 , Ømega$ intrinsic impedance, and require an antenna-like device to transfer them into the open air, characterized by an intrinsic impedance of $Z_textout = 377 , Ømega$ and a temperature of $T_textout simeq 300$ K, with minimal losses. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure we find the optimal shape of the impedance is exponential, and we adjust this shape to an analytical function. Additionally, this study reveals that losses are very sensitive to this shape, and small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work will impact the fields of quantum sensing and quantum metrology, as well as any open-air microwave quantum communication protocol, with special application to the development of the quantum radar.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a fridge, where they are created, into an environment dominated by thermal noise. Indeed, the states that carry such quantum resources are generated in a cryostat at $T_textin simeq 10^-2 $~K and with $Z_textin = 50 , Ømega$ intrinsic impedance, and require an antenna-like device to transfer them into the open air, characterized by an intrinsic impedance of $Z_textout = 377 , Ømega$ and a temperature of $T_textout simeq 300$ K, with minimal losses. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure we find the optimal shape of the impedance is exponential, and we adjust this shape to an analytical function. Additionally, this study reveals that losses are very sensitive to this shape, and small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work will impact the fields of quantum sensing and quantum metrology, as well as any open-air microwave quantum communication protocol, with special application to the development of the quantum radar. |

Kokkoniemi, R; Girard, J P; Hazra, D; Laitinen, A; Govenius, J; Lake, R E; Sallinen, I; Vesterinen, V; Hakonen, P; Möttönen, M Bolometer operating at the threshold for circuit quantum electrodynamics Journal Article 2020. @article{Kokkoniemi2020, title = {Bolometer operating at the threshold for circuit quantum electrodynamics}, author = {R Kokkoniemi and J P Girard and D Hazra and A Laitinen and J Govenius and R E Lake and I Sallinen and V Vesterinen and P Hakonen and M Möttönen}, year = {2020}, date = {2020-08-11}, abstract = {Radiation sensors based on the heating effect of the absorbed radiation are typically relatively simple to operate and flexible in terms of the input frequency. Consequently, they are widely applied, for example, in gas detection, security, THz imaging, astrophysical observations, and medical applications. A new spectrum of important applications is currently emerging from quantum technology and especially from electrical circuits behaving quantum mechanically. This circuit quantum electrodynamics (cQED) has given rise to unprecedented single-photon detectors and a quantum computer supreme to the classical supercomputers in a certain task. Thermal sensors are appealing in enhancing these devices since they are not plagued by quantum noise and are smaller, simpler, and consume about six orders of magnitude less power than the commonly used traveling-wave parametric amplifiers. However, despite great progress in the speed and noise levels of thermal sensors, no bolometer to date has proven fast and sensitive enough to provide advantages in cQED. Here, we experimentally demonstrate a bolometer surpassing this threshold with a noise equivalent power of $30, rmzW/sqrtrmHz$ on par with the current record while providing two-orders of magnitude shorter thermal time constant of 500 ns. Importantly, both of these characteristic numbers have been measured directly from the same device, which implies a faithful estimation of the calorimetric energy resolution of a single 30-GHz photon. These improvements stem from the utilization of a graphene monolayer as the active material with extremely low specific heat. The minimum demonstrated time constant of 200 ns falls greatly below the state-of-the-art dephasing times of roughly 100 mus for superconducting qubits and meets the timescales of contemporary readout schemes thus enabling the utilization of thermal detectors in cQED.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Radiation sensors based on the heating effect of the absorbed radiation are typically relatively simple to operate and flexible in terms of the input frequency. Consequently, they are widely applied, for example, in gas detection, security, THz imaging, astrophysical observations, and medical applications. A new spectrum of important applications is currently emerging from quantum technology and especially from electrical circuits behaving quantum mechanically. This circuit quantum electrodynamics (cQED) has given rise to unprecedented single-photon detectors and a quantum computer supreme to the classical supercomputers in a certain task. Thermal sensors are appealing in enhancing these devices since they are not plagued by quantum noise and are smaller, simpler, and consume about six orders of magnitude less power than the commonly used traveling-wave parametric amplifiers. However, despite great progress in the speed and noise levels of thermal sensors, no bolometer to date has proven fast and sensitive enough to provide advantages in cQED. Here, we experimentally demonstrate a bolometer surpassing this threshold with a noise equivalent power of $30, rmzW/sqrtrmHz$ on par with the current record while providing two-orders of magnitude shorter thermal time constant of 500 ns. Importantly, both of these characteristic numbers have been measured directly from the same device, which implies a faithful estimation of the calorimetric energy resolution of a single 30-GHz photon. These improvements stem from the utilization of a graphene monolayer as the active material with extremely low specific heat. The minimum demonstrated time constant of 200 ns falls greatly below the state-of-the-art dephasing times of roughly 100 mus for superconducting qubits and meets the timescales of contemporary readout schemes thus enabling the utilization of thermal detectors in cQED. |

Peronnin, T; ć, Markovi D; Ficheux, Q; Huard, B Sequential Dispersive Measurement of a Superconducting Qubit Journal Article Physical Review Letters, 124 (18), pp. 180502, 2020, ISSN: 0031-9007. @article{Peronnin2020, title = {Sequential Dispersive Measurement of a Superconducting Qubit}, author = {T Peronnin and D Markovi{ć} and Q Ficheux and B Huard}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.180502}, doi = {10.1103/PhysRevLett.124.180502}, issn = {0031-9007}, year = {2020}, date = {2020-05-01}, journal = {Physical Review Letters}, volume = {124}, number = {18}, pages = {180502}, publisher = {American Physical Society}, abstract = {We present a superconducting device that realizes the sequential measurement of a transmon qubit. The device disables common limitations of dispersive readout such as Purcell effect or transients in the cavity mode by turning on and off the coupling to the measurement channel on demand. The qubit measurement begins by loading a readout resonator that is coupled to the qubit. After an optimal interaction time with negligible loss, a microwave pump releases the content of the readout mode by upconversion into a measurement line in a characteristic time as low as 10 ns, which is 400 times shorter than the lifetime of the readout resonator. A direct measurement of the released field quadratures demonstrates a readout fidelity of 97.5% in a total measurement time of 220 ns. The Wigner tomography of the readout mode allows us to characterize the non-Gaussian nature of the readout mode and its dynamics.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a superconducting device that realizes the sequential measurement of a transmon qubit. The device disables common limitations of dispersive readout such as Purcell effect or transients in the cavity mode by turning on and off the coupling to the measurement channel on demand. The qubit measurement begins by loading a readout resonator that is coupled to the qubit. After an optimal interaction time with negligible loss, a microwave pump releases the content of the readout mode by upconversion into a measurement line in a characteristic time as low as 10 ns, which is 400 times shorter than the lifetime of the readout resonator. A direct measurement of the released field quadratures demonstrates a readout fidelity of 97.5% in a total measurement time of 220 ns. The Wigner tomography of the readout mode allows us to characterize the non-Gaussian nature of the readout mode and its dynamics. |

Olivares-Sánchez, J; Casanova, J; Solano, E; Lamata, L Measurement-Based Adaptation Protocol with Quantum Reinforcement Learning in a Rigetti Quantum Computer Journal Article Quantum Reports, 2 (2), pp. 293–304, 2020. @article{OlivaresSanchez2020, title = {Measurement-Based Adaptation Protocol with Quantum Reinforcement Learning in a Rigetti Quantum Computer}, author = {J Olivares-Sánchez and J Casanova and E Solano and L Lamata}, doi = {10.3390/quantum2020019}, year = {2020}, date = {2020-05-01}, journal = {Quantum Reports}, volume = {2}, number = {2}, pages = {293--304}, publisher = {MDPI AG}, abstract = {We present an experimental realisation of a measurement-based adaptation protocol with quantum reinforcement learning in a Rigetti cloud quantum computer. The experiment in this few-qubit superconducting chip faithfully reproduces the theoretical proposal, setting the first steps towards a semiautonomous quantum agent. This experiment paves the way towards quantum reinforcement learning with superconducting circuits.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present an experimental realisation of a measurement-based adaptation protocol with quantum reinforcement learning in a Rigetti cloud quantum computer. The experiment in this few-qubit superconducting chip faithfully reproduces the theoretical proposal, setting the first steps towards a semiautonomous quantum agent. This experiment paves the way towards quantum reinforcement learning with superconducting circuits. |

Hu, F; Lamata, L; Sanz, M; Chen, X; Chen, X; Wang, C; Solano, E Quantum computing cryptography: Finding cryptographic Boolean functions with quantum annealing by a 2000 qubit D-wave quantum computer Journal Article Physics Letters, Section A: General, Atomic and Solid State Physics, 384 (10), pp. 126214, 2020, ISSN: 0375-9601. @article{Hu2020, title = {Quantum computing cryptography: Finding cryptographic Boolean functions with quantum annealing by a 2000 qubit D-wave quantum computer}, author = {F Hu and L Lamata and M Sanz and X Chen and X Chen and C Wang and E Solano}, doi = {10.1016/j.physleta.2019.126214}, issn = {0375-9601}, year = {2020}, date = {2020-04-01}, journal = {Physics Letters, Section A: General, Atomic and Solid State Physics}, volume = {384}, number = {10}, pages = {126214}, publisher = {Elsevier B.V.}, abstract = {As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of n-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size O(22n) of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small n cases in a D-Wave machine, showing its capacity of devising cryptographic Boolean functions with certain relevant properties. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy.}, keywords = {}, pubstate = {published}, tppubtype = {article} } As the building block in symmetric cryptography, designing Boolean functions satisfying multiple properties is an important problem in sequence ciphers, block ciphers, and hash functions. However, the search of n-variable Boolean functions fulfilling global cryptographic constraints is computationally hard due to the super-exponential size O(22n) of the space. Here, we introduce a codification of the cryptographically relevant constraints in the ground state of an Ising Hamiltonian, allowing us to naturally encode it in a quantum annealer, which seems to provide a quantum speedup. Additionally, we benchmark small n cases in a D-Wave machine, showing its capacity of devising cryptographic Boolean functions with certain relevant properties. We have complemented it with local search and chain repair to improve the D-Wave quantum annealer performance related to the low connectivity. This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy. |

Dassonneville, R; Assouly, R; Peronnin, T; Rouchon, P; Huard, B Number-resolved photocounter for propagating microwave mode Miscellaneous 2020. @misc{Dassonneville2020a, title = {Number-resolved photocounter for propagating microwave mode}, author = {R Dassonneville and R Assouly and T Peronnin and P Rouchon and B Huard}, url = {http://arxiv.org/abs/2004.05114}, year = {2020}, date = {2020-04-01}, abstract = {Detectors of propagating microwave photons have recently been realized using superconducting circuits. However a number-resolved photocounter is still missing. In this letter, we demonstrate a single-shot counter for propagating microwave photons that can resolve up to $3$ photons. It is based on a pumped Josephson Ring Modulator that can catch an arbitrary propagating mode by frequency conversion and store its quantum state in a stationary memory mode. A transmon qubit then counts the number of photons in the memory mode using a series of binary questions. Using measurement based feedback, the number of questions is minimal and scales logarithmically with the maximal number of photons. The detector features a detection efficiency of $0.96 pm 0.04$, and a dark count probability of $0.030 pm 0.002$ for an average dead time of $4.5simmathrmmu s$. To maximize its performance, the device is first used as an emphin situ waveform detector from which an optimal pump is computed and applied. Depending on the number of incoming photons, the detector succeeds with a probability that ranges from $56%$ to $99%$.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Detectors of propagating microwave photons have recently been realized using superconducting circuits. However a number-resolved photocounter is still missing. In this letter, we demonstrate a single-shot counter for propagating microwave photons that can resolve up to $3$ photons. It is based on a pumped Josephson Ring Modulator that can catch an arbitrary propagating mode by frequency conversion and store its quantum state in a stationary memory mode. A transmon qubit then counts the number of photons in the memory mode using a series of binary questions. Using measurement based feedback, the number of questions is minimal and scales logarithmically with the maximal number of photons. The detector features a detection efficiency of $0.96 pm 0.04$, and a dark count probability of $0.030 pm 0.002$ for an average dead time of $4.5simmathrmmu s$. To maximize its performance, the device is first used as an emphin situ waveform detector from which an optimal pump is computed and applied. Depending on the number of incoming photons, the detector succeeds with a probability that ranges from $56%$ to $99%$. |

Ding, Y; Martín-Guerrero, J D; Sanz, M; Magdalena-Benedicto, R; Chen, X; Solano, E Retrieving Quantum Information with Active Learning Journal Article Physical Review Letters, 124 (14), pp. 140504, 2020, ISSN: 0031-9007. @article{Ding2020, title = {Retrieving Quantum Information with Active Learning}, author = {Y Ding and J D Martín-Guerrero and M Sanz and R Magdalena-Benedicto and X Chen and E Solano}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.140504}, doi = {10.1103/PhysRevLett.124.140504}, issn = {0031-9007}, year = {2020}, date = {2020-04-01}, journal = {Physical Review Letters}, volume = {124}, number = {14}, pages = {140504}, publisher = {American Physical Society (APS)}, abstract = {Active learning is a machine learning method aiming at optimal design for model training. At variance with supervised learning, which labels all samples, active learning provides an improved model by labeling samples with maximal uncertainty according to the estimation model. Here, we propose the use of active learning for efficient quantum information retrieval, which is a crucial task in the design of quantum experiments. Meanwhile, when dealing with large data output, we employ active learning for the sake of classification with minimal cost in fidelity loss. Indeed, labeling only 5% samples, we achieve almost 90% rate estimation. The introduction of active learning methods in the data analysis of quantum experiments will enhance applications of quantum technologies.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Active learning is a machine learning method aiming at optimal design for model training. At variance with supervised learning, which labels all samples, active learning provides an improved model by labeling samples with maximal uncertainty according to the estimation model. Here, we propose the use of active learning for efficient quantum information retrieval, which is a crucial task in the design of quantum experiments. Meanwhile, when dealing with large data output, we employ active learning for the sake of classification with minimal cost in fidelity loss. Indeed, labeling only 5% samples, we achieve almost 90% rate estimation. The introduction of active learning methods in the data analysis of quantum experiments will enhance applications of quantum technologies. |

Goes, B O; Landi, G T; Solano, E; Sanz, M; Céleri, L C Wehrl entropy production rate across a dynamical quantum phase transition Miscellaneous 2020. @misc{Goes2020, title = {Wehrl entropy production rate across a dynamical quantum phase transition}, author = {B O Goes and G T Landi and E Solano and M Sanz and L C Céleri}, url = {http://arxiv.org/abs/2004.01126}, year = {2020}, date = {2020-04-01}, abstract = {The quench dynamics of many-body quantum systems may exhibit non-analyticities in the Loschmidt echo, a phenomenon known as dynamical phase transition (DPT). Despite considerable research into the underlying mechanisms behind this phenomenon, several open questions still remain. Motivated by this, we put forth a detailed study of DPTs from the perspective of quantum phase space and entropy production, a key concept in thermodynamics. We focus on the Lipkin-Meshkov-Glick model and use spin coherent states to construct the corresponding Husimi-$Q$ quasi-probability distribution. The entropy of the $Q$-function, known as Wehrl entropy, provides a measure of the coarse-grained dynamics of the system and, therefore, evolves non-trivially even for closed systems. We show that critical quenches lead to a quasi-monotonic growth of the Wehrl entropy in time, combined with small oscillations. The former reflects the information scrambling characteristic of these transitions and serves as a measure of entropy production. On the other hand, the small oscillations imply negative entropy production rates and, therefore, signal the recurrences of the Loschmidt echo. Finally, we also study a Gaussification of the model based on a modified Holstein-Primakoff approximation. This allows us to identify the relative contribution of the low energy sector to the emergence of DPTs. The results presented in this article are relevant not only from the dynamical quantum phase transition perspective, but also for the field of quantum thermodynamics, since they point out that the Wehrl entropy can be used as a viable measure of entropy production.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The quench dynamics of many-body quantum systems may exhibit non-analyticities in the Loschmidt echo, a phenomenon known as dynamical phase transition (DPT). Despite considerable research into the underlying mechanisms behind this phenomenon, several open questions still remain. Motivated by this, we put forth a detailed study of DPTs from the perspective of quantum phase space and entropy production, a key concept in thermodynamics. We focus on the Lipkin-Meshkov-Glick model and use spin coherent states to construct the corresponding Husimi-$Q$ quasi-probability distribution. The entropy of the $Q$-function, known as Wehrl entropy, provides a measure of the coarse-grained dynamics of the system and, therefore, evolves non-trivially even for closed systems. We show that critical quenches lead to a quasi-monotonic growth of the Wehrl entropy in time, combined with small oscillations. The former reflects the information scrambling characteristic of these transitions and serves as a measure of entropy production. On the other hand, the small oscillations imply negative entropy production rates and, therefore, signal the recurrences of the Loschmidt echo. Finally, we also study a Gaussification of the model based on a modified Holstein-Primakoff approximation. This allows us to identify the relative contribution of the low energy sector to the emergence of DPTs. The results presented in this article are relevant not only from the dynamical quantum phase transition perspective, but also for the field of quantum thermodynamics, since they point out that the Wehrl entropy can be used as a viable measure of entropy production. |

Zhang, J; Li, T; Kokkoniemi, R; Yan, C; Liu, W; Partanen, M; Tan, K Y; He, M; Ji, L; Grönberg, L; Möttönen, M Broadband Tunable Phase Shifter For Microwaves Miscellaneous 2020. @misc{Zhang2020, title = {Broadband Tunable Phase Shifter For Microwaves}, author = {J Zhang and T Li and R Kokkoniemi and C Yan and W Liu and M Partanen and K Y Tan and M He and L Ji and L Grönberg and M Möttönen}, url = {http://arxiv.org/abs/2003.01356}, year = {2020}, date = {2020-03-01}, abstract = {We implement a broadly tunable phase shifter for microwaves based on superconducting quantum interference devices (SQUIDs) and study it both experimentally and theoretically. At different frequencies, a unit transmission coefficient, $|S_21|=1$, can be theoretically achieved along a curve where the phase shift is controllable by magnetic flux. The fabricated device consists of three equidistant SQUIDs interrupting a transmission line. We model each SQUID embedded at different positions along the transmission line with two parameters, capacitance and inductance, the values of which we extract from the experiments. In our experiments, the tunability of the phase shift varies from from $0.07timespi$ to $0.14timespi$ radians along the full-transmission curve with the input frequency ranging from 6.00 to 6.28$sim$GHz. The reported measurements are in good agreement with simulations, which is promising for future design work of phase shifters for different applications.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } We implement a broadly tunable phase shifter for microwaves based on superconducting quantum interference devices (SQUIDs) and study it both experimentally and theoretically. At different frequencies, a unit transmission coefficient, $|S_21|=1$, can be theoretically achieved along a curve where the phase shift is controllable by magnetic flux. The fabricated device consists of three equidistant SQUIDs interrupting a transmission line. We model each SQUID embedded at different positions along the transmission line with two parameters, capacitance and inductance, the values of which we extract from the experiments. In our experiments, the tunability of the phase shift varies from from $0.07timespi$ to $0.14timespi$ radians along the full-transmission curve with the input frequency ranging from 6.00 to 6.28$sim$GHz. The reported measurements are in good agreement with simulations, which is promising for future design work of phase shifters for different applications. |

Cong, L; Felicetti, S; Casanova, J; Lamata, L; Solano, E; Arrazola, I Selective interactions in the quantum Rabi model Journal Article Physical Review A, 101 (3), pp. 032350, 2020, ISSN: 2469-9926. @article{Cong2020, title = {Selective interactions in the quantum Rabi model}, author = {L Cong and S Felicetti and J Casanova and L Lamata and E Solano and I Arrazola}, url = {https://link.aps.org/doi/10.1103/PhysRevA.101.032350}, doi = {10.1103/PhysRevA.101.032350}, issn = {2469-9926}, year = {2020}, date = {2020-03-01}, journal = {Physical Review A}, volume = {101}, number = {3}, pages = {032350}, publisher = {American Physical Society}, abstract = {We demonstrate the emergence of selective k-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counterrotating terms produces multiphoton interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these k-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We demonstrate the emergence of selective k-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counterrotating terms produces multiphoton interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these k-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters. |

Capela, M; Céleri, L C; Modi, K; Chaves, R Monogamy of temporal correlations: Witnessing non-Markovianity beyond data processing Journal Article Physical Review Research, 2 (1), pp. 013350, 2020. @article{Capela2020, title = {Monogamy of temporal correlations: Witnessing non-Markovianity beyond data processing}, author = {M Capela and L C Céleri and K Modi and R Chaves}, doi = {10.1103/physrevresearch.2.013350}, year = {2020}, date = {2020-03-01}, journal = {Physical Review Research}, volume = {2}, number = {1}, pages = {013350}, publisher = {American Physical Society (APS)}, abstract = {The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements. |

Munuera-Javaloy, C; Arrazola, I; Solano, E; Casanova, J Double quantum magnetometry at large static magnetic fields Journal Article Physical Review B, 101 (10), pp. 104411, 2020, ISSN: 2469-9950. @article{Munuera-Javaloy2020, title = {Double quantum magnetometry at large static magnetic fields}, author = {C Munuera-Javaloy and I Arrazola and E Solano and J Casanova}, url = {https://link.aps.org/doi/10.1103/PhysRevB.101.104411}, doi = {10.1103/PhysRevB.101.104411}, issn = {2469-9950}, year = {2020}, date = {2020-03-01}, journal = {Physical Review B}, volume = {101}, number = {10}, pages = {104411}, publisher = {American Physical Society}, abstract = {We present a protocol to achieve double quantum magnetometry at large static magnetic fields. This is a regime where sensitive sample parameters, such as the chemical shift, get enhanced facilitating their characterization. In particular, our method delivers two-Tone stroboscopic radiation patterns with modulated Rabi frequencies to achieve larger spectral signals. Furthermore, it does not introduce inhomogeneous broadening in the sample spectrum preventing signal misinterpretation. Moreover, our protocol is designed to work under realistic conditions such as the presence of moderate microwave power and errors on the radiation fields. Albeit we particularize to nitrogen vacancy centers, our protocol is general, thus applicable to distinct quantum sensors.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a protocol to achieve double quantum magnetometry at large static magnetic fields. This is a regime where sensitive sample parameters, such as the chemical shift, get enhanced facilitating their characterization. In particular, our method delivers two-Tone stroboscopic radiation patterns with modulated Rabi frequencies to achieve larger spectral signals. Furthermore, it does not introduce inhomogeneous broadening in the sample spectrum preventing signal misinterpretation. Moreover, our protocol is designed to work under realistic conditions such as the presence of moderate microwave power and errors on the radiation fields. Albeit we particularize to nitrogen vacancy centers, our protocol is general, thus applicable to distinct quantum sensors. |

Ban, Y; Chen, X; Torrontegui, E; Solano, E; Casanova, J Speed-up Quantum Perceptron via Shortcuts to Adiabaticity Miscellaneous 2020. @misc{Ban2020, title = {Speed-up Quantum Perceptron via Shortcuts to Adiabaticity}, author = {Y Ban and X Chen and E Torrontegui and E Solano and J Casanova}, url = {http://arxiv.org/abs/2003.09938}, year = {2020}, date = {2020-03-01}, abstract = {The quantum perceptron is a fundamental building block in the area of quantum machine learning. This is a multidisciplinary field that incorporates properties of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where the control field on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function. This results in faster overall perceptron performance compared to quasi-adiabatic protocols, as well as in enhanced robustness against imperfections in the external control.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The quantum perceptron is a fundamental building block in the area of quantum machine learning. This is a multidisciplinary field that incorporates properties of quantum computing, such as state superposition and entanglement, to classical machine learning schemes. Motivated by the techniques of shortcuts to adiabaticity, we propose a speed-up quantum perceptron where the control field on the perceptron is inversely engineered leading to a rapid nonlinear response with a sigmoid activation function. This results in faster overall perceptron performance compared to quasi-adiabatic protocols, as well as in enhanced robustness against imperfections in the external control. |

Puebla, R; Ban, Y; Haase, J F; Plenio, M B; Paternostro, M; Casanova, J Versatile Atomic Magnetometry Assisted by Bayesian Inference Miscellaneous 2020. @misc{Puebla2020, title = {Versatile Atomic Magnetometry Assisted by Bayesian Inference}, author = {R Puebla and Y Ban and J F Haase and M B Plenio and M Paternostro and J Casanova}, url = {http://arxiv.org/abs/2003.02151}, year = {2020}, date = {2020-03-01}, abstract = {Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an $^171$Yb$^+$ trapped-ion quantum sensor but stress the general applicability of this approach to different systems.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Quantum sensors typically translate external fields into a periodic response whose frequency is then determined by analyses performed in Fourier space. This allows for a linear inference of the parameters that characterize external signals. In practice, however, quantum sensors are able to detect fields only in a narrow range of amplitudes and frequencies. A departure from this range, as well as the presence of significant noise sources and short detection times, lead to a loss of the linear relationship between the response of the sensor and the target field, thus limiting the working regime of the sensor. Here we address these challenges by means of a Bayesian inference approach that is tolerant to strong deviations from desired periodic responses of the sensor and is able to provide reliable estimates even with a very limited number of measurements. We demonstrate our method for an $^171$Yb$^+$ trapped-ion quantum sensor but stress the general applicability of this approach to different systems. |

Wang, Z -Y; Casanova, J; Plenio, M B Enhancing the robustness of dynamical decoupling sequences with correlated random phases Miscellaneous 2020. @misc{Wang2020a, title = {Enhancing the robustness of dynamical decoupling sequences with correlated random phases}, author = {Z -Y Wang and J Casanova and M B Plenio}, url = {http://arxiv.org/abs/2003.13453}, year = {2020}, date = {2020-03-01}, abstract = {We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $pi$ pulse imperfections and spurious responses due to finite-width $pi$ pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } We show that the addition of correlated phases to the recently developed method of randomized dynamical decoupling pulse sequences can improve its performance in quantum sensing. In particular, by correlating the relative phases of basic pulse units in dynamical decoupling sequences, we are able to improve the suppression of the signal distortion due to $pi$ pulse imperfections and spurious responses due to finite-width $pi$ pulses. This enhances the selectivity of quantum sensors such as those based on NV centers in diamond. |

Parra-Rodriguez, A; Lougovski, P; Lamata, L; Solano, E; Sanz, M Digital-analog quantum computation Journal Article Physical Review A, 101 (2), pp. 022305, 2020, ISSN: 2469-9926. @article{Parra-Rodriguez2020, title = {Digital-analog quantum computation}, author = {A Parra-Rodriguez and P Lougovski and L Lamata and E Solano and M Sanz}, url = {https://link.aps.org/doi/10.1103/PhysRevA.101.022305}, doi = {10.1103/PhysRevA.101.022305}, issn = {2469-9926}, year = {2020}, date = {2020-02-01}, journal = {Physical Review A}, volume = {101}, number = {2}, pages = {022305}, abstract = {Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. We construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods. |

Gonzalez-Raya, T; Lukens, J M; Céleri, L C; Sanz, M Quantum Memristors in Frequency-Entangled Optical Fields Journal Article Materials, 13 (4), pp. 864, 2020, ISSN: 1996-1944. @article{Gonzalez-Raya2020a, title = {Quantum Memristors in Frequency-Entangled Optical Fields}, author = {T Gonzalez-Raya and J M Lukens and L C Céleri and M Sanz}, url = {https://www.mdpi.com/1996-1944/13/4/864}, doi = {10.3390/ma13040864}, issn = {1996-1944}, year = {2020}, date = {2020-02-01}, journal = {Materials}, volume = {13}, number = {4}, pages = {864}, publisher = {Multidisciplinary Digital Publishing Institute}, abstract = {A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A quantum memristor is a passive resistive circuit element with memory, engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequency-entangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work could be a building block for constructing quantum neural networks in quantum photonics, when scaling up. |

Silva, F; Sanz, M; Seixas, J; Solano, E; Omar, Y Perceptrons from memristors Journal Article Neural Networks, 122 , pp. 273–278, 2020, ISSN: 1879-2782. @article{Silva2020, title = {Perceptrons from memristors}, author = {F Silva and M Sanz and J Seixas and E Solano and Y Omar}, doi = {10.1016/j.neunet.2019.10.013}, issn = {1879-2782}, year = {2020}, date = {2020-02-01}, journal = {Neural Networks}, volume = {122}, pages = {273--278}, publisher = {Elsevier Ltd}, abstract = {Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Papert's theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Papert's theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms. |

Headley, D; Müller, T; Martin, A; Solano, E; Sanz, M; Wilhelm, F K Approximating the Quantum Approximate Optimisation Algorithm Miscellaneous 2020. @misc{Headley2020, title = {Approximating the Quantum Approximate Optimisation Algorithm}, author = {D Headley and T Müller and A Martin and E Solano and M Sanz and F K Wilhelm}, url = {http://arxiv.org/abs/2002.12215}, year = {2020}, date = {2020-02-01}, abstract = {The Quantum Approximate Optimisation Algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The Quantum Approximate Optimisation Algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the post-supremacy, noisy, intermediate scale era of quantum computing. In this work, we exploit the recently proposed digital-analog quantum computation paradigm, in which the versatility of programmable universal quantum computers and the error resilience of quantum simulators are combined to improve platforms for quantum computation. We show that the digital-analog paradigm is suited to the variational quantum approximate optimisation algorithm, due to its inherent resilience against coherent errors, by performing large-scale simulations and providing analytical bounds for its performance in devices with finite single-qubit operation times. We observe regimes of single-qubit operation speed in which the considered variational algorithm provides a significant improvement over non-variational counterparts. |

Huang, T -Y; Malomed, B A; Chen, X Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation Miscellaneous 2020. @misc{Huang2020d, title = {Shortcuts to adiabaticity for an interacting Bose-Einstein condensate via exact solutions of the generalized Ermakov equation}, author = {T -Y Huang and B A Malomed and X Chen}, url = {http://arxiv.org/abs/2002.03632}, year = {2020}, date = {2020-02-01}, abstract = {Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator trap is investigated by combining techniques of the variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabacity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help to address fundamental problems of the quantum speed limit and thermodynamics.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Shortcuts to adiabatic expansion of the effectively one-dimensional Bose-Einstein condensate (BEC) loaded in the harmonic-oscillator trap is investigated by combining techniques of the variational approximation and inverse engineering. Piecewise-constant (discontinuous) intermediate trap frequencies, similar to the known bang-bang forms in the optimal-control theory, are derived from an exact solution of a generalized Ermakov equation. Taking into regard the BEC's intrinsic nonlinearity, results are reported for the minimal transfer time, excitation energy (which measures deviation from the effective adiabacity), and stability for the shortcut-to-adiabaticity protocols. These results are not only useful for the realization of fast frictionless cooling, but also help to address fundamental problems of the quantum speed limit and thermodynamics. |

Osada, T; Coutinho, B; Omar, Y; Sanaka, K; Munro, W J; Nemoto, K Continuous-time quantum-walk spatial search on the Bollobás scale-free network Journal Article Physical Review A, 101 (2), pp. 022310, 2020, ISSN: 2469-9934. @article{Osada2020, title = {Continuous-time quantum-walk spatial search on the Bollobás scale-free network}, author = {T Osada and B Coutinho and Y Omar and K Sanaka and W J Munro and K Nemoto}, doi = {10.1103/PhysRevA.101.022310}, issn = {2469-9934}, year = {2020}, date = {2020-02-01}, journal = {Physical Review A}, volume = {101}, number = {2}, pages = {022310}, publisher = {American Physical Society}, abstract = {The scale-free property emerges in various real-world networks and is an essential property that characterizes the dynamics or features of such networks. In this work, we investigate the effect of this scale-free property on a quantum information processing task of finding a marked node in the network, known as the quantum spatial search. We analyze the quantum spatial search algorithm using a continuous-time quantum walk on the Bollobás network, and we evaluate the time T to localize the quantum walker on the marked node starting from an unbiased initial state. Our main finding is that T is determined by the global structure around the marked node, while some local information of the marked node, such as the degree, does not identify T. We discuss this by examining the correlation between T and some centrality measures of the network, and we show that the closeness centrality of the marked node is highly correlated with T. We also characterize the distribution of T by marking different nodes in the network, which displays a multimode log-normal distribution. Especially on the Bollobás network, T is a few orders of magnitude shorter depending on whether the marked node is adjacent to the largest degree hub node. However, as T depends on the property of the marked node, one requires some amount of prior knowledge about such a property of the marked node in order to identify the optimal time to measure the quantum walker and achieve a fast search. These results indicate that the existence of the hub node in the scale-free network plays a crucial role in the quantum spatial search.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The scale-free property emerges in various real-world networks and is an essential property that characterizes the dynamics or features of such networks. In this work, we investigate the effect of this scale-free property on a quantum information processing task of finding a marked node in the network, known as the quantum spatial search. We analyze the quantum spatial search algorithm using a continuous-time quantum walk on the Bollobás network, and we evaluate the time T to localize the quantum walker on the marked node starting from an unbiased initial state. Our main finding is that T is determined by the global structure around the marked node, while some local information of the marked node, such as the degree, does not identify T. We discuss this by examining the correlation between T and some centrality measures of the network, and we show that the closeness centrality of the marked node is highly correlated with T. We also characterize the distribution of T by marking different nodes in the network, which displays a multimode log-normal distribution. Especially on the Bollobás network, T is a few orders of magnitude shorter depending on whether the marked node is adjacent to the largest degree hub node. However, as T depends on the property of the marked node, one requires some amount of prior knowledge about such a property of the marked node in order to identify the optimal time to measure the quantum walker and achieve a fast search. These results indicate that the existence of the hub node in the scale-free network plays a crucial role in the quantum spatial search. |

Arrazola, I; Plenio, M B; Solano, E; Casanova, J Hybrid Microwave-Radiation Patterns for High-Fidelity Quantum Gates with Trapped Ions Journal Article Physical Review Applied, 13 (2), pp. 024068, 2020, ISSN: 2331-7019. @article{Arrazola2020, title = {Hybrid Microwave-Radiation Patterns for High-Fidelity Quantum Gates with Trapped Ions}, author = {I Arrazola and M B Plenio and E Solano and J Casanova}, url = {https://link.aps.org/doi/10.1103/PhysRevApplied.13.024068}, doi = {10.1103/PhysRevApplied.13.024068}, issn = {2331-7019}, year = {2020}, date = {2020-02-01}, journal = {Physical Review Applied}, volume = {13}, number = {2}, pages = {024068}, publisher = {American Physical Society}, abstract = {We present a method that combines continuous and pulsed microwave-radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $pi$ pulses. This leads to high-fidelity entangling gates that are resilient against magnetic field fluctuations, changes in the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensities. We demonstrate the performance of our method with detailed numerical simulations that take into account the main sources of decoherence.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a method that combines continuous and pulsed microwave-radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $pi$ pulses. This leads to high-fidelity entangling gates that are resilient against magnetic field fluctuations, changes in the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensities. We demonstrate the performance of our method with detailed numerical simulations that take into account the main sources of decoherence. |

Ding, Y:; Huang, T; Hao, M; Chen, X Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap Miscellaneous 2020. @misc{Ding2020a, title = {Smooth bang-bang shortcuts to adiabaticity for atomic transport in a moving harmonic trap}, author = {Y: Ding and T Huang and M Hao and X Chen}, url = {http://arxiv.org/abs/2002.11605}, year = {2020}, date = {2020-02-01}, abstract = {Bang-bang optimization, as a shortcut to adiabaticity, provides a simple but fast protocol allowing high-fidelity shuttling of cold atoms or trapped ions, with the wide applications in interferometry, metrology, and quantum information processing. Such time-optimal control with at least two discontinuous switches requires the sudden jumps, which costs extra efforts and harms the overall performance as well. To circumvent these problems, we investigate the smooth bang-bang protocols with near-minimal time for fast atomic transport in a moving harmonic trap. Smoothing is accomplished by the Pontryagin's maximal principle with the constraint that limits the first and second derivatives of control input. Moreover, the multiple shooting method is numerically presented for a smoothing procedure for the minimal-time optimization with the same constraints. By numerical examples and comparisons, we conclude that the smooth control input is capable of eliminating the energy excitation and sloshing amplitude at the cost of a slight increase in minimal time. Our smooth bang-bang protocols presented here are more practical and feasible in the relevant experiments, and can be easily extended to other classical and quantum systems where the shortcuts to adiabaticity are requested and implemented.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Bang-bang optimization, as a shortcut to adiabaticity, provides a simple but fast protocol allowing high-fidelity shuttling of cold atoms or trapped ions, with the wide applications in interferometry, metrology, and quantum information processing. Such time-optimal control with at least two discontinuous switches requires the sudden jumps, which costs extra efforts and harms the overall performance as well. To circumvent these problems, we investigate the smooth bang-bang protocols with near-minimal time for fast atomic transport in a moving harmonic trap. Smoothing is accomplished by the Pontryagin's maximal principle with the constraint that limits the first and second derivatives of control input. Moreover, the multiple shooting method is numerically presented for a smoothing procedure for the minimal-time optimization with the same constraints. By numerical examples and comparisons, we conclude that the smooth control input is capable of eliminating the energy excitation and sloshing amplitude at the cost of a slight increase in minimal time. Our smooth bang-bang protocols presented here are more practical and feasible in the relevant experiments, and can be easily extended to other classical and quantum systems where the shortcuts to adiabaticity are requested and implemented. |

Gonzalez-Raya, T; Solano, E; Sanz, M Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials Journal Article Quantum, 4 , pp. 224, 2020, ISSN: 2521-327X. @article{Gonzalez-Raya2020b, title = {Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials}, author = {T Gonzalez-Raya and E Solano and M Sanz}, url = {https://quantum-journal.org/papers/q-2020-01-20-224/}, doi = {10.22331/q-2020-01-20-224}, issn = {2521-327X}, year = {2020}, date = {2020-01-01}, journal = {Quantum}, volume = {4}, pages = {224}, publisher = {Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften}, abstract = {The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise. |

Martin, A; Lamata, L; Solano, E; Sanz, M Digital-analog quantum algorithm for the quantum Fourier transform Journal Article Physical Review Research, 2 (1), pp. 013012, 2020. @article{Martin2020, title = {Digital-analog quantum algorithm for the quantum Fourier transform}, author = {A Martin and L Lamata and E Solano and M Sanz}, doi = {10.1103/physrevresearch.2.013012}, year = {2020}, date = {2020-01-01}, journal = {Physical Review Research}, volume = {2}, number = {1}, pages = {013012}, publisher = {American Physical Society (APS)}, abstract = {Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy. |

Häffner, T; Zanin, G L; Gomes, R M; Céleri, L C; Souto Ribeiro, P H Remote preparation of single photon vortex thermal states Miscellaneous 2020. @misc{Haeffner2020, title = {Remote preparation of single photon vortex thermal states}, author = {T Häffner and G L Zanin and R M Gomes and L C Céleri and P H {Souto Ribeiro}}, url = {http://arxiv.org/abs/2001.08178}, year = {2020}, date = {2020-01-01}, abstract = {Photon pairs produced in spontaneous parametric down-conversion are naturally entangled in their transverse spatial degrees of freedom including the orbital angular momentum. Pumping a non-linear crystal with a zero order Gaussian mode produces quantum correlated signal and idler photons with equal orbital angular momentum and opposite signs. Measurements performed on one of the photons prepares the state of the other remotely. We study the remote state preparation in this system from the perspective of its potential application to Quantum Thermodynamics.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Photon pairs produced in spontaneous parametric down-conversion are naturally entangled in their transverse spatial degrees of freedom including the orbital angular momentum. Pumping a non-linear crystal with a zero order Gaussian mode produces quantum correlated signal and idler photons with equal orbital angular momentum and opposite signs. Measurements performed on one of the photons prepares the state of the other remotely. We study the remote state preparation in this system from the perspective of its potential application to Quantum Thermodynamics. |

Borim, D; Céleri, L C; Kiosses, V I Precision in estimating Unruh temperature Miscellaneous 2020. @misc{Borim2020, title = {Precision in estimating Unruh temperature}, author = {D Borim and L C Céleri and V I Kiosses}, url = {http://arxiv.org/abs/2001.09085}, year = {2020}, date = {2020-01-01}, abstract = {The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, one of which is inertial while the other one undergoes acceleration. Our results show that the maximum of the Fisher information, thus characterizing the maximum possible precision according to Crammér-Rao bound, occurs only for small accelerations, while it decreases fast when acceleration increases. Moreover, the role of initial coherence ---in the single detector case---, or entanglement ---in the two detectors case---, is to decrease Fisher information. Therefore, under the considered protocol, internal coherence (or entanglement) is not a resource for estimating Unruh temperature. These unexpected results show that a detection of the Unruh effect can be even more challenge than previously thought. Finally, by considering the connection between Unruh effect and Hawking radiation, we discuss how our results can be understood in the context of the estimation of Hawking temperature.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The goal of quantum metrology is the exploitation of quantum resources, like entanglement or quantum coherence, in the fundamental task of parameter estimation. Here we consider the question of the estimation of the Unruh temperature in the scenario of relativistic quantum metrology. Specifically, we study two distinct cases. First, a single Unruh-DeWitt detector interacting with a scalar quantum field undergoes an uniform acceleration for a finite amount of proper time, and the role of coherence in the estimation process is analyzed. After this, we consider two initially entangled detectors, one of which is inertial while the other one undergoes acceleration. Our results show that the maximum of the Fisher information, thus characterizing the maximum possible precision according to Crammér-Rao bound, occurs only for small accelerations, while it decreases fast when acceleration increases. Moreover, the role of initial coherence ---in the single detector case---, or entanglement ---in the two detectors case---, is to decrease Fisher information. Therefore, under the considered protocol, internal coherence (or entanglement) is not a resource for estimating Unruh temperature. These unexpected results show that a detection of the Unruh effect can be even more challenge than previously thought. Finally, by considering the connection between Unruh effect and Hawking radiation, we discuss how our results can be understood in the context of the estimation of Hawking temperature. |

## 2019 |

Kokkoniemi, R; Govenius, J; Vesterinen, V; Lake, R E; Gunyhó, A M; Tan, K Y; Simbierowicz, S; Grönberg, L; Lehtinen, J; Prunnila, M; Hassel, J; Lamminen, A; Saira, O -P; Möttönen, M Nanobolometer with ultralow noise equivalent power Journal Article Communications Physics, 2 (1), pp. 124, 2019, ISSN: 2399-3650. @article{Kokkoniemi2019, title = {Nanobolometer with ultralow noise equivalent power}, author = {R Kokkoniemi and J Govenius and V Vesterinen and R E Lake and A M Gunyhó and K Y Tan and S Simbierowicz and L Grönberg and J Lehtinen and M Prunnila and J Hassel and A Lamminen and O -P Saira and M Möttönen}, url = {http://www.nature.com/articles/s42005-019-0225-6}, doi = {10.1038/s42005-019-0225-6}, issn = {2399-3650}, year = {2019}, date = {2019-12-01}, journal = {Communications Physics}, volume = {2}, number = {1}, pages = {124}, publisher = {Nature Publishing Group}, abstract = {Since the introduction of bolometers more than a century ago, they have been used in various applications ranging from chemical sensors, consumer electronics, and security to particle physics and astronomy. However, faster bolometers with lower noise are of great interest from the fundamental point of view and to find new use-cases for this versatile concept. We demonstrate a nanobolometer that exhibits roughly an order of magnitude lower noise equivalent power, 20zW/Hz, than previously reported for any bolometer. Importantly, it is more than an order of magnitude faster than other low-noise bolometers, with a time constant of 30 mu s at 60zW/Hz. These results suggest a calorimetric energy resolution of 0.3 zJ = h x 0.4 THz with a time constant of 30 mu s. Further development of this nanobolometer may render it a promising candidate for future applications requiring extremely low noise and high speed such as those in quantum technology and terahertz photon counting.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Since the introduction of bolometers more than a century ago, they have been used in various applications ranging from chemical sensors, consumer electronics, and security to particle physics and astronomy. However, faster bolometers with lower noise are of great interest from the fundamental point of view and to find new use-cases for this versatile concept. We demonstrate a nanobolometer that exhibits roughly an order of magnitude lower noise equivalent power, 20zW/Hz, than previously reported for any bolometer. Importantly, it is more than an order of magnitude faster than other low-noise bolometers, with a time constant of 30 mu s at 60zW/Hz. These results suggest a calorimetric energy resolution of 0.3 zJ = h x 0.4 THz with a time constant of 30 mu s. Further development of this nanobolometer may render it a promising candidate for future applications requiring extremely low noise and high speed such as those in quantum technology and terahertz photon counting. |

Galicia, A; Ramon, B; Solano, E; Sanz, M Enhanced connectivity of quantum hardware with digital-analog control Miscellaneous 2019. @misc{Galicia2019, title = {Enhanced connectivity of quantum hardware with digital-analog control}, author = {A Galicia and B Ramon and E Solano and M Sanz}, url = {http://arxiv.org/abs/1912.09331}, year = {2019}, date = {2019-12-01}, abstract = {Quantum computers based on superconducting circuits are experiencing a rapid development, aiming at outperforming classical computers in certain useful tasks in the near future. However, the currently available chip fabrication technologies limit the capability of gathering a large number of high-quality qubits in a single superconducting chip, a requirement for implementing quantum error correction. Furthermore, achieving high connectivity in a chip poses a formidable technological challenge. Here, we propose a hybrid digital-analog quantum algorithm that enhances the physical connectivity among qubits coupled by an arbitrary inhomogeneous nearest-neighbour Ising Hamiltonian and generates an arbitrary all-to-all Ising Hamiltonian only by employing single-qubit rotations. Additionally, we optimize the proposed algorithm in the number of analog blocks and in the time required for the simulation. These results take advantage of the natural evolution of the system by combining the flexibility of digital steps with the robustness of analog quantum computing, allowing us to improve the connectivity of the hardware and the efficiency of quantum algorithms.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Quantum computers based on superconducting circuits are experiencing a rapid development, aiming at outperforming classical computers in certain useful tasks in the near future. However, the currently available chip fabrication technologies limit the capability of gathering a large number of high-quality qubits in a single superconducting chip, a requirement for implementing quantum error correction. Furthermore, achieving high connectivity in a chip poses a formidable technological challenge. Here, we propose a hybrid digital-analog quantum algorithm that enhances the physical connectivity among qubits coupled by an arbitrary inhomogeneous nearest-neighbour Ising Hamiltonian and generates an arbitrary all-to-all Ising Hamiltonian only by employing single-qubit rotations. Additionally, we optimize the proposed algorithm in the number of analog blocks and in the time required for the simulation. These results take advantage of the natural evolution of the system by combining the flexibility of digital steps with the robustness of analog quantum computing, allowing us to improve the connectivity of the hardware and the efficiency of quantum algorithms. |

Chen, Q -M; Deppe, F; Wu, R -B; Sun, L; Liu, Y -x; Nojiri, Y; Pogorzalek, S; Renger, M; Partanen, M; Fedorov, K G; Marx, A; Gross, R Quantum Fourier Transform in Oscillating Modes Miscellaneous 2019. @misc{Chen2019c, title = {Quantum Fourier Transform in Oscillating Modes}, author = {Q -M Chen and F Deppe and R -B Wu and L Sun and Y -x Liu and Y Nojiri and S Pogorzalek and M Renger and M Partanen and K G Fedorov and A Marx and R Gross}, url = {http://arxiv.org/abs/1912.09861}, year = {2019}, date = {2019-12-01}, abstract = {Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates are used to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits. In this work, we explore a novel approach based on resonators that forms a high-dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to a single resonator, and obtain the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. A quantitive analysis shows that our method allows for high-dimensional and fully-quantum QFT employing the state-of-the-art superconducting quantum circuits. This paves the way for implementing various QFT related quantum algorithms.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Quantum Fourier transform (QFT) is a key ingredient of many quantum algorithms. In typical applications such as phase estimation, a considerable number of ancilla qubits and gates are used to form a Hilbert space large enough for high-precision results. Qubit recycling reduces the number of ancilla qubits to one, but it is only applicable to semi-classical QFT and requires repeated measurements and feedforward within the coherence time of the qubits. In this work, we explore a novel approach based on resonators that forms a high-dimensional Hilbert space for the realization of QFT. By employing the perfect state-transfer method, we map an unknown multi-qubit state to a single resonator, and obtain the QFT state in the second oscillator through cross-Kerr interaction and projective measurement. A quantitive analysis shows that our method allows for high-dimensional and fully-quantum QFT employing the state-of-the-art superconducting quantum circuits. This paves the way for implementing various QFT related quantum algorithms. |

Barrios, G A; Retamal, J C; Solano, E; Sanz, M Analog simulator of integro-differential equations with classical memristors Journal Article Scientific Reports, 9 (1), pp. 12928, 2019, ISSN: 2045-2322. @article{Barrios2019, title = {Analog simulator of integro-differential equations with classical memristors}, author = {G A Barrios and J C Retamal and E Solano and M Sanz}, doi = {10.1038/s41598-019-49204-y}, issn = {2045-2322}, year = {2019}, date = {2019-12-01}, journal = {Scientific Reports}, volume = {9}, number = {1}, pages = {12928}, publisher = {Nature Publishing Group}, abstract = {An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.}, keywords = {}, pubstate = {published}, tppubtype = {article} } An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-differential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales. |

Eneriz, H; Rossatto, D Z; Cárdenas-López, F A; Solano, E; Sanz, M Degree of Quantumness in Quantum Synchronization Journal Article Scientific Reports, 9 (1), pp. 19933, 2019, ISSN: 2045-2322. @article{Eneriz2019, title = {Degree of Quantumness in Quantum Synchronization}, author = {H Eneriz and D Z Rossatto and F A Cárdenas-López and E Solano and M Sanz}, url = {http://www.nature.com/articles/s41598-019-56468-x}, doi = {10.1038/s41598-019-56468-x}, issn = {2045-2322}, year = {2019}, date = {2019-12-01}, journal = {Scientific Reports}, volume = {9}, number = {1}, pages = {19933}, publisher = {Nature Research}, abstract = {We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum nature of synchronization in quantum systems. Following techniques from quantum information, we propose the number of non-commuting observables that synchronize as a measure of quantumness. This figure of merit is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate it in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities. Moreover, we study the synchronization of the expectation values of the Pauli operators and we propose a feasible superconducting circuit setup. Finally, we discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators. |

Gutiérrez, M J; Berrocal, J; Domínguez, F; Arrazola, I; Block, M; Solano, E; Rodríguez, D Dynamics of an unbalanced two-ion crystal in a Penning trap for application in optical mass spectrometry Journal Article Physical Review A, 100 (6), pp. 063415, 2019, ISSN: 2469-9926. @article{Gutierrez2019, title = {Dynamics of an unbalanced two-ion crystal in a Penning trap for application in optical mass spectrometry}, author = {M J Gutiérrez and J Berrocal and F Domínguez and I Arrazola and M Block and E Solano and D Rodríguez}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.063415}, doi = {10.1103/PhysRevA.100.063415}, issn = {2469-9926}, year = {2019}, date = {2019-12-01}, journal = {Physical Review A}, volume = {100}, number = {6}, pages = {063415}, publisher = {American Physical Society}, abstract = {In this paper, the dynamics of an unbalanced two-ion crystal comprising the "target" and the "sensor" ions confined in a Penning trap along the magnetic-field axis has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron, and reduced-cyclotron modes split up into the so-called stretch and common modes, that are generalizations of the well-known "breathing" and "center-of-mass" motions of a balanced crystal made of two ions. By using optical detection to measure the frequencies of the modes of the crystal, and of the sensor ion on its own, in the quantum regime of motion, it will be possible to determine the target ion's free-cyclotron frequency. The nonharmonicity of the Coulomb interaction is also discussed since this causes large systematic effects, which are minimized due to the high sensitivity of the optical detection method when the crystal is cooled to the ground state of motion in the Penning trap.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, the dynamics of an unbalanced two-ion crystal comprising the "target" and the "sensor" ions confined in a Penning trap along the magnetic-field axis has been studied. First, the low amplitude regime is addressed. In this regime, the overall potential including the Coulomb repulsion between the ions can be considered harmonic and the axial, magnetron, and reduced-cyclotron modes split up into the so-called stretch and common modes, that are generalizations of the well-known "breathing" and "center-of-mass" motions of a balanced crystal made of two ions. By using optical detection to measure the frequencies of the modes of the crystal, and of the sensor ion on its own, in the quantum regime of motion, it will be possible to determine the target ion's free-cyclotron frequency. The nonharmonicity of the Coulomb interaction is also discussed since this causes large systematic effects, which are minimized due to the high sensitivity of the optical detection method when the crystal is cooled to the ground state of motion in the Penning trap. |

Peng, J; Rico, E; Zhong, J; Solano, E; Egusquiza, I L Unified superradiant phase transitions Journal Article Physical Review A, 100 (6), pp. 063820, 2019, ISSN: 2469-9926. @article{Peng2019, title = {Unified superradiant phase transitions}, author = {J Peng and E Rico and J Zhong and E Solano and I L Egusquiza}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.063820}, doi = {10.1103/PhysRevA.100.063820}, issn = {2469-9926}, year = {2019}, date = {2019-12-01}, journal = {Physical Review A}, volume = {100}, number = {6}, pages = {063820}, publisher = {American Physical Society}, abstract = {We prove that superradiant phase transitions (SPTs) of the Dicke model and its generalizations in the thermodynamic and classical oscillator limit are indeed of the same type. In this sense, we unify SPTs under both limits at zero and finite temperature. We show that the mean-field approximation for bosons is exact in both cases, and compute the structure and location of the phase transitions in parameter space using a concise analytic method. Moreover, we illustrate how SPT properties (first order, second order, or none) are related to symmetry. Finally, we uncover general features of the phase structure in the space of parameters of these models with dipolar couplings. There will be a region of normal phase in the neighborhood of the origin of the space of dipolar couplings, and that generally one flows radially in this space to a superradiant phase.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We prove that superradiant phase transitions (SPTs) of the Dicke model and its generalizations in the thermodynamic and classical oscillator limit are indeed of the same type. In this sense, we unify SPTs under both limits at zero and finite temperature. We show that the mean-field approximation for bosons is exact in both cases, and compute the structure and location of the phase transitions in parameter space using a concise analytic method. Moreover, we illustrate how SPT properties (first order, second order, or none) are related to symmetry. Finally, we uncover general features of the phase structure in the space of parameters of these models with dipolar couplings. There will be a region of normal phase in the neighborhood of the origin of the space of dipolar couplings, and that generally one flows radially in this space to a superradiant phase. |

ñ, Ba M C; Blatt, R; Catani, J; Celi, A; Cirac, J I; Dalmonte, M; Fallani, L; Jansen, K; Lewenstein, M; Montangero, S; Muschik, C A; Reznik, B; Rico, E; Tagliacozzo, L; Van Acoleyen, K; Verstraete, F; Wiese, U -J; Wingate, M; Zakrzewski, J; Zoller, P Simulating Lattice Gauge Theories within Quantum Technologies Miscellaneous 2019. @misc{Banuls2019, title = {Simulating Lattice Gauge Theories within Quantum Technologies}, author = {M C Ba{ñ}uls and R Blatt and J Catani and A Celi and J I Cirac and M Dalmonte and L Fallani and K Jansen and M Lewenstein and S Montangero and C A Muschik and B Reznik and E Rico and L Tagliacozzo and K {Van Acoleyen} and F Verstraete and U -J Wiese and M Wingate and J Zakrzewski and P Zoller}, url = {http://arxiv.org/abs/1911.00003}, year = {2019}, date = {2019-10-01}, abstract = {Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented - a classical simulation approach - applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. |

Mera, B; Sacha, K; Omar, Y Topologically Protected Quantization of Work Journal Article Physical Review Letters, 123 (2), pp. 020601, 2019, ISSN: 0031-9007. @article{Mera2019, title = {Topologically Protected Quantization of Work}, author = {B Mera and K Sacha and Y Omar}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.020601}, doi = {10.1103/PhysRevLett.123.020601}, issn = {0031-9007}, year = {2019}, date = {2019-07-01}, journal = {Physical Review Letters}, volume = {123}, number = {2}, pages = {020601}, publisher = {American Physical Society}, abstract = {The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here, we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is topologically protected. We illustrate this phenomenon with the example of an atom whose center of mass motion is coupled to its internal degrees of freedom by electromagnetic waves.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this amount of work, when averaged over a single temporal period of the potential, can take any value in a continuous fashion. Here, we present a topological effect inducing the quantization of the average work. We find that this work is equal to the first Chern number calculated in a unit cell of a space-time lattice. Hence, this quantization of the average work is topologically protected. We illustrate this phenomenon with the example of an atom whose center of mass motion is coupled to its internal degrees of freedom by electromagnetic waves. |

Ding, Y; Chen, X; Lamata, L; Solano, E; Sanz, M Logistic Network Design with a D-Wave Quantum Annealer Miscellaneous 2019. @misc{Ding2019, title = {Logistic Network Design with a D-Wave Quantum Annealer}, author = {Y Ding and X Chen and L Lamata and E Solano and M Sanz}, url = {http://arxiv.org/abs/1906.10074}, year = {2019}, date = {2019-06-01}, abstract = {Logistic network design is an abstract optimization problem which, under the assumption of minimal cost, determines the optimal configuration of infrastructures and facilities of the supply chain based on customer demand. With the solutions at hand, key economic decisions are taken about the location, number, as well as size of manufacturing facilities and warehouses. Therefore, an efficient method to address this question, which is known to be NP-hard, has relevant financial consequences. Here, we propose a hybrid classical-quantum annealing algorithm to accurately obtain the optimal solution. The cost function with constraints is translated to a spin Hamiltonian, whose ground state is supposed to encode the searched result. This algorithm is realized on a D-Wave quantum computer and positively compared with the results of the best classical optimization algorithms. This work shows that state-of-the-art quantum annealers may address useful chain supply problems.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Logistic network design is an abstract optimization problem which, under the assumption of minimal cost, determines the optimal configuration of infrastructures and facilities of the supply chain based on customer demand. With the solutions at hand, key economic decisions are taken about the location, number, as well as size of manufacturing facilities and warehouses. Therefore, an efficient method to address this question, which is known to be NP-hard, has relevant financial consequences. Here, we propose a hybrid classical-quantum annealing algorithm to accurately obtain the optimal solution. The cost function with constraints is translated to a spin Hamiltonian, whose ground state is supposed to encode the searched result. This algorithm is realized on a D-Wave quantum computer and positively compared with the results of the best classical optimization algorithms. This work shows that state-of-the-art quantum annealers may address useful chain supply problems. |

Arrazola, I; Solano, E; Casanova, J Selective hybrid spin interactions with low radiation power Journal Article Physical Review B, 99 (24), pp. 245405, 2019, ISSN: 2469-9950. @article{Arrazola2019, title = {Selective hybrid spin interactions with low radiation power}, author = {I Arrazola and E Solano and J Casanova}, url = {https://link.aps.org/doi/10.1103/PhysRevB.99.245405}, doi = {10.1103/PhysRevB.99.245405}, issn = {2469-9950}, year = {2019}, date = {2019-06-01}, journal = {Physical Review B}, volume = {99}, number = {24}, pages = {245405}, publisher = {American Physical Society}, abstract = {We present a protocol for designing appropriately extended $pi$ pulses that achieves tunable, thus selective, electron-nuclear spin interactions with low-driving radiation power. The latter is of great benefit when $pi$ pulses are displayed over biological samples as it reduces sample heating. Our method is general since it can be applied to different quantum sensor devices such as nitrogen vacancy centers or silicon vacancy centers. Furthermore, it can be directly incorporated in commonly used stroboscopic dynamical decoupling techniques to achieve enhanced nuclear selectivity and control, which demonstrates its flexibility.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a protocol for designing appropriately extended $pi$ pulses that achieves tunable, thus selective, electron-nuclear spin interactions with low-driving radiation power. The latter is of great benefit when $pi$ pulses are displayed over biological samples as it reduces sample heating. Our method is general since it can be applied to different quantum sensor devices such as nitrogen vacancy centers or silicon vacancy centers. Furthermore, it can be directly incorporated in commonly used stroboscopic dynamical decoupling techniques to achieve enhanced nuclear selectivity and control, which demonstrates its flexibility. |

Albarrán-Arriagada, F; Retamal, J C; Solano, E; Lamata, L Reinforcement learning for semi-autonomous approximate quantum eigensolver Journal Article Machine Learning: Science and Technology, 1 (1), pp. 015002, 2019. @article{Albarran-Arriagada2019, title = {Reinforcement learning for semi-autonomous approximate quantum eigensolver}, author = {F Albarrán-Arriagada and J C Retamal and E Solano and L Lamata}, url = {http://arxiv.org/abs/1906.06702 http://dx.doi.org/10.1088/2632-2153/ab43b4}, doi = {10.1088/2632-2153/ab43b4}, year = {2019}, date = {2019-06-01}, journal = {Machine Learning: Science and Technology}, volume = {1}, number = {1}, pages = {015002}, publisher = {IOP Publishing}, abstract = {The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix $hatU_E=e^-itauhatmathcalO_E$ where $hatmathcalO_E$ is a Hermitian operator, and $tau$ is a real parameter. The agent is a quantum state which adapts to some eigenvector of $hatmathcalO_E$ by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90% in less than 10 iterations, and surpass 98% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89% in 8000 iterations for a random operator, and fidelities of $99%$ for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The characterization of an operator by its eigenvectors and eigenvalues allows us to know its action over any quantum state. Here, we propose a protocol to obtain an approximation of the eigenvectors of an arbitrary Hermitian quantum operator. This protocol is based on measurement and feedback processes, which characterize a reinforcement learning protocol. Our proposal is composed of two systems, a black box named environment and a quantum state named agent. The role of the environment is to change any quantum state by a unitary matrix $hatU_E=e^-itauhatmathcalO_E$ where $hatmathcalO_E$ is a Hermitian operator, and $tau$ is a real parameter. The agent is a quantum state which adapts to some eigenvector of $hatmathcalO_E$ by repeated interactions with the environment, feedback process, and semi-random rotations. With this proposal, we can obtain an approximation of the eigenvectors of a random qubit operator with average fidelity over 90% in less than 10 iterations, and surpass 98% in less than 300 iterations. Moreover, for the two-qubit cases, the four eigenvectors are obtained with fidelities above 89% in 8000 iterations for a random operator, and fidelities of $99%$ for an operator with the Bell states as eigenvectors. This protocol can be useful to implement semi-autonomous quantum devices which should be capable of extracting information and deciding with minimal resources and without human intervention. |

Agustí, A; Solano, E; Sabín, C Entanglement through qubit motion and the dynamical Casimir effect Journal Article Physical Review A, 99 (5), pp. 052328, 2019, ISSN: 2469-9926. @article{Agusti2019, title = {Entanglement through qubit motion and the dynamical Casimir effect}, author = {A Agustí and E Solano and C Sabín}, url = {http://arxiv.org/abs/1812.08554 http://dx.doi.org/10.1103/PhysRevA.99.052328 https://link.aps.org/doi/10.1103/PhysRevA.99.052328}, doi = {10.1103/PhysRevA.99.052328}, issn = {2469-9926}, year = {2019}, date = {2019-05-01}, journal = {Physical Review A}, volume = {99}, number = {5}, pages = {052328}, publisher = {American Physical Society}, abstract = {We explore the interplay between acceleration radiation and the dynamical Casimir effect in the field of superconducting quantum technologies, analyzing the generation of entanglement between two qubits by means of the dynamical Casimir effect in several states of qubit motion. We show that the correlated absorption and emission of photons are crucial for entanglement, which in some cases can be linked to the notion of simultaneity in special relativity.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We explore the interplay between acceleration radiation and the dynamical Casimir effect in the field of superconducting quantum technologies, analyzing the generation of entanglement between two qubits by means of the dynamical Casimir effect in several states of qubit motion. We show that the correlated absorption and emission of photons are crucial for entanglement, which in some cases can be linked to the notion of simultaneity in special relativity. |

Puebla, R; Zicari, G; Arrazola, I; Solano, E; Paternostro, M; Casanova, J Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models Journal Article Symmetry, 11 (5), pp. 695, 2019, ISSN: 2073-8994. @article{Puebla2019b, title = {Spin-Boson Model as A Simulator of Non-Markovian Multiphoton Jaynes-Cummings Models}, author = {R Puebla and G Zicari and I Arrazola and E Solano and M Paternostro and J Casanova}, url = {https://www.mdpi.com/2073-8994/11/5/695}, doi = {10.3390/sym11050695}, issn = {2073-8994}, year = {2019}, date = {2019-05-01}, journal = {Symmetry}, volume = {11}, number = {5}, pages = {695}, publisher = {MDPI AG}, abstract = {The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms. |

Ding, Y; Lamata, L; Martín-Guerrero, J D; Lizaso, E; Mugel, S; Chen, Xi; ú, Or R; Solano, E; Sanz, M Towards Prediction of Financial Crashes with a D-Wave Quantum Computer Miscellaneous 2019. @misc{Ding2019b, title = {Towards Prediction of Financial Crashes with a D-Wave Quantum Computer}, author = {Y Ding and L Lamata and J D Martín-Guerrero and E Lizaso and S Mugel and Xi Chen and R Or{ú}s and E Solano and M Sanz}, url = {http://arxiv.org/abs/1904.05808}, year = {2019}, date = {2019-04-01}, abstract = {Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed to a spin-$1/2$ Hamiltonian with at most two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. Our experiment paves the way to study quantitative macroeconomics, enlarging the number of problems that can be handled by current quantum computers.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed to a spin-$1/2$ Hamiltonian with at most two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. Our experiment paves the way to study quantitative macroeconomics, enlarging the number of problems that can be handled by current quantum computers. |

Cárdenas-López, F; Romero, G; Lamata, L; Solano, E; Retamal, J C Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics Journal Article Symmetry, 11 (3), pp. 372, 2019, ISSN: 2073-8994. @article{Cardenas-Lopez2019, title = {Parity-Assisted Generation of Nonclassical States of Light in Circuit Quantum Electrodynamics}, author = {F Cárdenas-López and G Romero and L Lamata and E Solano and J C Retamal}, url = {https://www.mdpi.com/2073-8994/11/3/372}, doi = {10.3390/sym11030372}, issn = {2073-8994}, year = {2019}, date = {2019-03-01}, journal = {Symmetry}, volume = {11}, number = {3}, pages = {372}, publisher = {Multidisciplinary Digital Publishing Institute}, keywords = {}, pubstate = {published}, tppubtype = {article} } |

Yu, S; Albarrán-Arriagada, F; Retamal, J C; Wang, Y -T; Liu, W; Ke, Z -J; Meng, Y; Li, Z -P; Tang, J -S; Solano, E; Lamata, L; Li, C -F; Guo, G -C Reconstruction of a Photonic Qubit State with Reinforcement Learning Journal Article Advanced Quantum Technologies, pp. 1800074, 2019, ISSN: 2511-9044. @article{Yu2019, title = {Reconstruction of a Photonic Qubit State with Reinforcement Learning}, author = {S Yu and F Albarrán-Arriagada and J C Retamal and Y -T Wang and W Liu and Z -J Ke and Y Meng and Z -P Li and J -S Tang and E Solano and L Lamata and C -F Li and G -C Guo}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/qute.201800074}, doi = {10.1002/qute.201800074}, issn = {2511-9044}, year = {2019}, date = {2019-03-01}, journal = {Advanced Quantum Technologies}, pages = {1800074}, publisher = {John Wiley & Sons, Ltd}, abstract = {An experiment is performed to reconstruct an unknown photonic quantum state with a limited amount of copies. A semi-quantum reinforcement learning approach is employed to adapt one qubit state, an ägent," to an unknown quantum state, an "environment," by successive single-shot measurements and feedback, in order to achieve maximum overlap. The experimental learning device herein, composed of a quantum photonics setup, can adjust the corresponding parameters to rotate the agent system based on the measurement outcomes "0" or "1" in the environment (i.e., reward/punishment signals). The results show that, when assisted by such a quantum machine learning technique, fidelities of the deterministic single-photon agent states can achieve over 88% under a proper reward/punishment ratio within 50 iterations. This protocol offers a tool for reconstructing an unknown quantum state when only limited copies are provided, and can also be extended to higher dimensions, multipartite, and mixed quantum state scenarios.}, keywords = {}, pubstate = {published}, tppubtype = {article} } An experiment is performed to reconstruct an unknown photonic quantum state with a limited amount of copies. A semi-quantum reinforcement learning approach is employed to adapt one qubit state, an ägent," to an unknown quantum state, an "environment," by successive single-shot measurements and feedback, in order to achieve maximum overlap. The experimental learning device herein, composed of a quantum photonics setup, can adjust the corresponding parameters to rotate the agent system based on the measurement outcomes "0" or "1" in the environment (i.e., reward/punishment signals). The results show that, when assisted by such a quantum machine learning technique, fidelities of the deterministic single-photon agent states can achieve over 88% under a proper reward/punishment ratio within 50 iterations. This protocol offers a tool for reconstructing an unknown quantum state when only limited copies are provided, and can also be extended to higher dimensions, multipartite, and mixed quantum state scenarios. |

Parra-Rodriguez, A; Egusquiza, I L; DiVincenzo, D P; Solano, E Canonical circuit quantization with linear nonreciprocal devices Journal Article Physical Review B, 99 (1), pp. 014514, 2019. @article{Parra-Rodriguez2019, title = {Canonical circuit quantization with linear nonreciprocal devices}, author = {A Parra-Rodriguez and I L Egusquiza and D P DiVincenzo and E Solano}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.014514}, doi = {10.1103/PhysRevB.99.014514}, year = {2019}, date = {2019-01-01}, journal = {Physical Review B}, volume = {99}, number = {1}, pages = {014514}, publisher = {American Physical Society}, abstract = {Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general nonreciprocal networks on the quantum regime. We apply it to pedagogical and pathological examples of circuits containing Josephson junctions and ideal nonreciprocal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on nonreciprocal devices characterized by impedance or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and nonreciprocal devices.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general nonreciprocal networks on the quantum regime. We apply it to pedagogical and pathological examples of circuits containing Josephson junctions and ideal nonreciprocal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on nonreciprocal devices characterized by impedance or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and nonreciprocal devices. |

Puebla, R; Casanova, J; Houhou, O; Solano, E; Paternostro, M Quantum simulation of multiphoton and nonlinear dissipative spin-boson models Journal Article Physical Review A, 99 (3), pp. 032303, 2019, ISSN: 2469-9926. @article{Puebla2019a, title = {Quantum simulation of multiphoton and nonlinear dissipative spin-boson models}, author = {R Puebla and J Casanova and O Houhou and E Solano and M Paternostro}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.032303}, doi = {10.1103/PhysRevA.99.032303}, issn = {2469-9926}, year = {2019}, date = {2019-01-01}, journal = {Physical Review A}, volume = {99}, number = {3}, pages = {032303}, publisher = {American Physical Society}, abstract = {We present a framework for the realization of dissipative evolutions of spin-boson models, including multiphoton exchange dynamics, as well as nonlinear transition rates. Our approach is based on the implementation of a generalized version of a dissipative linear quantum Rabi model. The latter comprises a linearly coupled spin-boson term, spin rotations, and standard dissipators. We provide numerical simulations of illustrative cases supporting the good performance of our method. Our work allows for the simulation of a large class of fundamentally different quantum models where the effect of distinct dissipative processes can be easily investigated.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We present a framework for the realization of dissipative evolutions of spin-boson models, including multiphoton exchange dynamics, as well as nonlinear transition rates. Our approach is based on the implementation of a generalized version of a dissipative linear quantum Rabi model. The latter comprises a linearly coupled spin-boson term, spin rotations, and standard dissipators. We provide numerical simulations of illustrative cases supporting the good performance of our method. Our work allows for the simulation of a large class of fundamentally different quantum models where the effect of distinct dissipative processes can be easily investigated. |

Alaeian, H; Chang, C W S; Moghaddam, M V; Wilson, C M; Solano, E; Rico, E Creating lattice gauge potentials in circuit QED: The bosonic Creutz ladder Journal Article Physical Review A, 99 (5), pp. 053834, 2019, ISSN: 2469-9926. @article{Alaeian2019, title = {Creating lattice gauge potentials in circuit QED: The bosonic Creutz ladder}, author = {H Alaeian and C W S Chang and M V Moghaddam and C M Wilson and E Solano and E Rico}, url = {https://link.aps.org/doi/10.1103/PhysRevA.99.053834}, doi = {10.1103/PhysRevA.99.053834}, issn = {2469-9926}, year = {2019}, date = {2019-01-01}, journal = {Physical Review A}, volume = {99}, number = {5}, pages = {053834}, publisher = {American Physical Society}, abstract = {In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The first scheme is based on coupled transmons whose on-site energies are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the phase difference between adjacent sites on creating a complex hopping rate between coupled qubits. The second method relies on the parametrically coupling the modes of a SQUID in a resonator and controlling the hopping phase via a coherent pump. Both proposals can be readily realized in a superconducting circuit with the existing technology and are suitable for scalable lattices. As an example benefiting from these complex-valued hopping terms, we simulated the behavior of a plaquette of bosonic Creutz ladder as one of the important models with interdisciplinary interest in various branches of physics. Our results clearly show the emergence of chiral edge modes and directional transport between lattice sites. Combined with intrinsic nonlinearity of the transmon qubits such lattices would be an ideal platform for simulating many different Hamiltonians such as the Bose-Hubbard model with nontrivial gauge fields. Important direct applications of the presented results span a broad range from signal processing in nonreciprocal transport to quantum simulation of gauge-invariant models in fundamental physics.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this work we propose two protocols to make an effective gauge potential for microwave photons in circuit QED. The first scheme is based on coupled transmons whose on-site energies are harmonically modulated in time. We investigate the effect of various types of capacitive and inductive couplings, and the role of the phase difference between adjacent sites on creating a complex hopping rate between coupled qubits. The second method relies on the parametrically coupling the modes of a SQUID in a resonator and controlling the hopping phase via a coherent pump. Both proposals can be readily realized in a superconducting circuit with the existing technology and are suitable for scalable lattices. As an example benefiting from these complex-valued hopping terms, we simulated the behavior of a plaquette of bosonic Creutz ladder as one of the important models with interdisciplinary interest in various branches of physics. Our results clearly show the emergence of chiral edge modes and directional transport between lattice sites. Combined with intrinsic nonlinearity of the transmon qubits such lattices would be an ideal platform for simulating many different Hamiltonians such as the Bose-Hubbard model with nontrivial gauge fields. Important direct applications of the presented results span a broad range from signal processing in nonreciprocal transport to quantum simulation of gauge-invariant models in fundamental physics. |

Hu, F; Lamata, L; Wang, C; Chen, X; Solano, E; Sanz, M Quantum Supremacy in Cryptography with a Low-Connectivity Quantum Annealer Miscellaneous 2019. @misc{Hu2019c, title = {Quantum Supremacy in Cryptography with a Low-Connectivity Quantum Annealer}, author = {F Hu and L Lamata and C Wang and X Chen and E Solano and M Sanz}, url = {http://arxiv.org/abs/1906.08140}, year = {2019}, date = {2019-01-01}, abstract = {The application in cryptography of quantum algorithms for prime factorization fostered the interest in quantum computing. However, quantum computers, and particularly quantum annealers, can also be helpful to construct secure cryptographic keys. Indeed, finding robust Boolean functions for cryptography is an important problem in sequence ciphers, block ciphers, and hash functions, among others. Due to the superexponential size O(22n) of the associated space, finding n-variable Boolean functions with global cryptographic constraints is computationally hard. This problem has already been addressed employing generic low-connected incoherent D-Wave quantum annealers. However, the limited connectivity of the Chimera graph, together with the exponential growth in the complexity of the Boolean-function design problem, limit the problem scalability. Here, we propose a special-purpose coherent quantum-annealing architecture with three couplers per qubit, designed to optimally encode the bent-function design problem. A coherent quantum annealer with this tree-type architecture has the potential to solve the eight-variable bent-function design problem, which is classically unsolved, with only 127 physical qubits and 126 couplers. This paves the way to reach useful quantum supremacy within the framework of quantum annealing for cryptographic purposes.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } The application in cryptography of quantum algorithms for prime factorization fostered the interest in quantum computing. However, quantum computers, and particularly quantum annealers, can also be helpful to construct secure cryptographic keys. Indeed, finding robust Boolean functions for cryptography is an important problem in sequence ciphers, block ciphers, and hash functions, among others. Due to the superexponential size O(22n) of the associated space, finding n-variable Boolean functions with global cryptographic constraints is computationally hard. This problem has already been addressed employing generic low-connected incoherent D-Wave quantum annealers. However, the limited connectivity of the Chimera graph, together with the exponential growth in the complexity of the Boolean-function design problem, limit the problem scalability. Here, we propose a special-purpose coherent quantum-annealing architecture with three couplers per qubit, designed to optimally encode the bent-function design problem. A coherent quantum annealer with this tree-type architecture has the potential to solve the eight-variable bent-function design problem, which is classically unsolved, with only 127 physical qubits and 126 couplers. This paves the way to reach useful quantum supremacy within the framework of quantum annealing for cryptographic purposes. |

Pogorzalek, S; Fedorov, K G; Xu, M; Parra-Rodriguez, A; Sanz, M; Fischer, M; Xie, E; Inomata, K; Nakamura, Y; Solano, E; Marx, A; Deppe, F; Gross, R Secure quantum remote state preparation of squeezed microwave states Journal Article Nature Communications, 10 (1), pp. 2604, 2019, ISSN: 2041-1723. @article{Pogorzalek2019a, title = {Secure quantum remote state preparation of squeezed microwave states}, author = {S Pogorzalek and K G Fedorov and M Xu and A Parra-Rodriguez and M Sanz and M Fischer and E Xie and K Inomata and Y Nakamura and E Solano and A Marx and F Deppe and R Gross}, url = {http://www.nature.com/articles/s41467-019-10727-7}, doi = {10.1038/s41467-019-10727-7}, issn = {2041-1723}, year = {2019}, date = {2019-01-01}, journal = {Nature Communications}, volume = {10}, number = {1}, pages = {2604}, publisher = {Nature Publishing Group}, abstract = {Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular, remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. Finally, security of remote state preparation is investigated by using the concept of the one-time pad and measuring the von Neumann entropies. We find nearly identical values for the entropy of the remotely prepared state and the respective conditional entropy given the classically communicated information and, thus, demonstrate close-to-perfect security.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum communication protocols based on nonclassical correlations can be more efficient than known classical methods and offer intrinsic security over direct state transfer. In particular, remote state preparation aims at the creation of a desired and known quantum state at a remote location using classical communication and quantum entanglement. We present an experimental realization of deterministic continuous-variable remote state preparation in the microwave regime over a distance of 35 cm. By employing propagating two-mode squeezed microwave states and feedforward, we achieve the remote preparation of squeezed states with up to 1.6 dB of squeezing below the vacuum level. Finally, security of remote state preparation is investigated by using the concept of the one-time pad and measuring the von Neumann entropies. We find nearly identical values for the entropy of the remotely prepared state and the respective conditional entropy given the classically communicated information and, thus, demonstrate close-to-perfect security. |

Martin, A; Candelas, B; Rodríguez-Rozas, Á; Martín-Guerrero, J D; Chen, X; Lamata, L; ú, Or R; Solano, E; Sanz, M Towards Pricing Financial Derivatives with an IBM Quantum Computer Miscellaneous 2019. @misc{Martin2019a, title = {Towards Pricing Financial Derivatives with an IBM Quantum Computer}, author = {A Martin and B Candelas and Á Rodríguez-Rozas and J D Martín-Guerrero and X Chen and L Lamata and R Or{ú}s and E Solano and M Sanz}, url = {http://arxiv.org/abs/1904.05803}, year = {2019}, date = {2019-01-01}, abstract = {Abstract Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. On its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the $5$-qubit IBMQX2 quantum computer for $2times 2$ and $3times 3$ cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This manuscript is a first step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future.}, keywords = {}, pubstate = {published}, tppubtype = {misc} } Abstract Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time-evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. On its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between the number of noisy factors considered and the computational time to perform a numerical simulation. Here, we employ the quantum principal component analysis to reduce the number of noisy factors required to accurately simulate the time evolution of several time-maturing forward rates. The principal components are experimentally estimated with the $5$-qubit IBMQX2 quantum computer for $2times 2$ and $3times 3$ cross-correlation matrices, which are based on historical data for two and three time-maturing forward rates. This manuscript is a first step towards the design of a general quantum algorithm to fully simulate on quantum computers the Heath-Jarrow-Morton model for pricing interest-rate financial derivatives. It shows indeed that practical applications of quantum computers in finance will be achievable in the near future. |