# 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

## 2019 |

Casanova, J; Torrontegui, E; Plenio, M B; García-Ripoll, J J; Solano, E Modulated Continuous Wave Control for Energy-Efficient Electron-Nuclear Spin Coupling Journal Article Physical Review Letters, 122 (1), pp. 010407, 2019, ISSN: 0031-9007. @article{Casanova2019, title = {Modulated Continuous Wave Control for Energy-Efficient Electron-Nuclear Spin Coupling}, author = {J Casanova and E Torrontegui and M B Plenio and J J García-Ripoll and E Solano}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.010407}, doi = {10.1103/PhysRevLett.122.010407}, issn = {0031-9007}, year = {2019}, date = {2019-01-01}, journal = {Physical Review Letters}, volume = {122}, number = {1}, pages = {010407}, publisher = {American Physical Society}, abstract = {We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts. Our controls are also suitable for quantum information processors and nuclear polarization schemes.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We develop energy efficient, continuous microwave schemes to couple electron and nuclear spins, using phase or amplitude modulation to bridge their frequency difference. These controls have promising applications in biological systems, where microwave power should be limited, as well as in situations with high Larmor frequencies due to large magnetic fields and nuclear magnetic moments. These include nanoscale NMR where high magnetic fields achieves enhanced thermal nuclear polarization and larger chemical shifts. Our controls are also suitable for quantum information processors and nuclear polarization schemes. |

Ding, Y; Lamata, L; Sanz, M; Chen, X; Solano, E Experimental Implementation of a Quantum Autoencoder via Quantum Adders Journal Article Advanced Quantum Technologies, pp. 1800065, 2019, ISSN: 2511-9044. @article{Ding2019a, title = {Experimental Implementation of a Quantum Autoencoder via Quantum Adders}, author = {Y Ding and L Lamata and M Sanz and X Chen and E Solano}, url = {http://doi.wiley.com/10.1002/qute.201800065}, doi = {10.1002/qute.201800065}, issn = {2511-9044}, year = {2019}, date = {2019-01-01}, journal = {Advanced Quantum Technologies}, pages = {1800065}, publisher = {John Wiley & Sons, Ltd}, abstract = {Quantum autoencoders allow for reducing the amount of resources in a quantum computation by mapping the original Hilbert space onto a reduced space with the relevant information. Recently, it was proposed to employ approximate quantum adders to implement quantum autoencoders in quantum technologies. Here, we carry out the experimental implementation of this proposal in the Rigetti cloud quantum computer employing up to three qubits. The experimental fidelities are in good agreement with the theoretical prediction, thus proving the feasibility to realize quantum autoencoders via quantum adders in state-of-the-art superconducting quantum technologies.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum autoencoders allow for reducing the amount of resources in a quantum computation by mapping the original Hilbert space onto a reduced space with the relevant information. Recently, it was proposed to employ approximate quantum adders to implement quantum autoencoders in quantum technologies. Here, we carry out the experimental implementation of this proposal in the Rigetti cloud quantum computer employing up to three qubits. The experimental fidelities are in good agreement with the theoretical prediction, thus proving the feasibility to realize quantum autoencoders via quantum adders in state-of-the-art superconducting quantum technologies. |

Cárdenas-López, F A; Sanz, M; Retamal, J C; Solano, E Enhanced Quantum Synchronization via Quantum Machine Learning Journal Article Advanced Quantum Technologies, pp. 1800076, 2019, ISSN: 2511-9044. @article{Cardenas-Lopez2019a, title = {Enhanced Quantum Synchronization via Quantum Machine Learning}, author = {F A Cárdenas-López and M Sanz and J C Retamal and E Solano}, url = {http://doi.wiley.com/10.1002/qute.201800076}, doi = {10.1002/qute.201800076}, issn = {2511-9044}, year = {2019}, date = {2019-01-01}, journal = {Advanced Quantum Technologies}, pages = {1800076}, publisher = {John Wiley & Sons, Ltd}, abstract = {We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in this digital-analog block decomposition the fundamental elements of a quantum machine learning protocol, in which the agent and the environment (learning units) interact through a mediating system, namely, the register. If we can additionally equip this algorithm with a classical feedback mechanism, which consists of projective measurements in the register, reinitialization of the register state and local conditional operations on the agent and environment subspace, a powerful and flexible quantum machine learning protocol emerges. Indeed, numerical simulations show that this protocol enhances the synchronization process, even when every subsystem experience different loss/decoherence mechanisms, and give us the flexibility to choose the synchronization state. Finally, we propose an implementation based on current technologies in superconducting circuits.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study the quantum synchronization between a pair of two-level systems inside two coupled cavities. By using a digital-analog decomposition of the master equation that rules the system dynamics, we show that this approach leads to quantum synchronization between both two-level systems. Moreover, we can identify in this digital-analog block decomposition the fundamental elements of a quantum machine learning protocol, in which the agent and the environment (learning units) interact through a mediating system, namely, the register. If we can additionally equip this algorithm with a classical feedback mechanism, which consists of projective measurements in the register, reinitialization of the register state and local conditional operations on the agent and environment subspace, a powerful and flexible quantum machine learning protocol emerges. Indeed, numerical simulations show that this protocol enhances the synchronization process, even when every subsystem experience different loss/decoherence mechanisms, and give us the flexibility to choose the synchronization state. Finally, we propose an implementation based on current technologies in superconducting circuits. |

Mäkinen, A; Ikonen, J; Partanen, M; Möttönen, M Reconstruction approach to quantum dynamics of bosonic systems Journal Article Physical Review A, 100 (4), pp. 042109, 2019, ISSN: 2469-9926. @article{Maekinen2019, title = {Reconstruction approach to quantum dynamics of bosonic systems}, author = {A Mäkinen and J Ikonen and M Partanen and M Möttönen}, url = {https://link.aps.org/doi/10.1103/PhysRevA.100.042109}, doi = {10.1103/PhysRevA.100.042109}, issn = {2469-9926}, year = {2019}, date = {2019-01-01}, journal = {Physical Review A}, volume = {100}, number = {4}, pages = {042109}, publisher = {American Physical Society}, abstract = {We propose an approach to analytically solve the quantum dynamics of bosonic systems. The method is based on reconstructing the quantum state of the system from the moments of its annihilation operators, dynamics of which is solved in the Heisenberg picture. The proposed dynamical reconstruction method is general in the sense that it does not require assumptions on the initial conditions of the system such as separability, or the structure of the system such as linearity. It is an alternative to the standard master-equation approaches, which are analytically demanding especially for large multipartite quantum systems. To demonstrate the proposed technique, we apply it to a system consisting of two coupled damped quantum harmonic oscillators.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We propose an approach to analytically solve the quantum dynamics of bosonic systems. The method is based on reconstructing the quantum state of the system from the moments of its annihilation operators, dynamics of which is solved in the Heisenberg picture. The proposed dynamical reconstruction method is general in the sense that it does not require assumptions on the initial conditions of the system such as separability, or the structure of the system such as linearity. It is an alternative to the standard master-equation approaches, which are analytically demanding especially for large multipartite quantum systems. To demonstrate the proposed technique, we apply it to a system consisting of two coupled damped quantum harmonic oscillators. |

Gonzalez-Raya, T; Cheng, X H; Egusquiza, I L; Chen, X; Sanz, M; Solano, E Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons Journal Article Physical Review Applied, 12 (1), pp. 014037, 2019, ISSN: 2331-7019. @article{Gonzalez-Raya2019, title = {Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons}, author = {T Gonzalez-Raya and X H Cheng and I L Egusquiza and X Chen and M Sanz and E Solano}, doi = {10.1103/PhysRevApplied.12.014037}, issn = {2331-7019}, year = {2019}, date = {2019-01-01}, journal = {Physical Review Applied}, volume = {12}, number = {1}, pages = {014037}, publisher = {American Physical Society}, abstract = {The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element; namely, capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. We consider a quantized Hodgkin-Huxley model based on a quantum-memristor formalism. We compare the behavior of the membrane voltage and the potassium-channel conductance when the circuit is subjected to ac sources, in both the classical realm and the quantum realm. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage shows purely quantum features related to the circuit zero-point energy. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf superconducting quantum-interference device in superconducting circuits. This study may allow the construction of quantum neuron networks inspired by the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element; namely, capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. We consider a quantized Hodgkin-Huxley model based on a quantum-memristor formalism. We compare the behavior of the membrane voltage and the potassium-channel conductance when the circuit is subjected to ac sources, in both the classical realm and the quantum realm. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage shows purely quantum features related to the circuit zero-point energy. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf superconducting quantum-interference device in superconducting circuits. This study may allow the construction of quantum neuron networks inspired by the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning. |

Sevriuk, V A; Tan, K Y; Hyyppä, E; Silveri, M; Partanen, M; Jenei, M; Masuda, S; Goetz, J; Vesterinen, V; Grönberg, L; Möttönen, M Fast control of dissipation in a superconducting resonator Journal Article Applied Physics Letters, 115 (8), pp. 082601, 2019, ISSN: 0003-6951. @article{Sevriuk2019, title = {Fast control of dissipation in a superconducting resonator}, author = {V A Sevriuk and K Y Tan and E Hyyppä and M Silveri and M Partanen and M Jenei and S Masuda and J Goetz and V Vesterinen and L Grönberg and M Möttönen}, url = {http://aip.scitation.org/doi/10.1063/1.5116659}, doi = {10.1063/1.5116659}, issn = {0003-6951}, year = {2019}, date = {2019-01-01}, journal = {Applied Physics Letters}, volume = {115}, number = {8}, pages = {082601}, publisher = {American Institute of Physics Inc.}, abstract = {We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory, it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active reset of a superconducting quantum circuit. In the future, a similar scheme can potentially be used to initialize superconducting quantum bits.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We report on fast tunability of an electromagnetic environment coupled to a superconducting coplanar waveguide resonator. Namely, we utilize a recently developed quantum-circuit refrigerator (QCR) to experimentally demonstrate a dynamic tunability in the total damping rate of the resonator up to almost two orders of magnitude. Based on the theory, it corresponds to a change in the internal damping rate by nearly four orders of magnitude. The control of the QCR is fully electrical, with the shortest implemented operation times in the range of 10 ns. This experiment constitutes a fast active reset of a superconducting quantum circuit. In the future, a similar scheme can potentially be used to initialize superconducting quantum bits. |

## 2018 |

Sanz, M; Fedorov, K G; Deppe, F; Solano, E Challenges in Open-air Microwave Quantum Communication and Sensing Inproceedings 2018 IEEE Conference on Antenna Measurements & Applications (CAMA), pp. 1–4, IEEE, 2018, ISBN: 978-1-5386-5795-9. @inproceedings{Sanz2018, title = {Challenges in Open-air Microwave Quantum Communication and Sensing}, author = {M Sanz and K G Fedorov and F Deppe and E Solano}, url = {https://ieeexplore.ieee.org/document/8530599/}, doi = {10.1109/CAMA.2018.8530599}, isbn = {978-1-5386-5795-9}, year = {2018}, date = {2018-01-01}, booktitle = {2018 IEEE Conference on Antenna Measurements & Applications (CAMA)}, pages = {1--4}, publisher = {IEEE}, abstract = {Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological advances have been reached in the last years, such as the first quantum communication between ground and satellites, as well as the first proof-of-principle experiments in quantum sensing. The development of microwave quantum technologies turned out, nonetheless, to be more challenging. Here, we will discuss the challenges regarding the use of microwaves for quantum communication and sensing. Based on this analysis, we propose a roadmap to achieve real-life applications in these fields.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } Quantum communication is a holy grail to achieve secure communication among a set of partners, since it is provably unbreakable by physical laws. Quantum sensing employs quantum entanglement as an extra resource to determine parameters by either using less resources or attaining a precision unachievable in classical protocols. A paradigmatic example is the quantum radar, which allows one to detect an object without being detected oneself, by making use of the additional asset provided by quantum entanglement to reduce the intensity of the signal. In the optical regime, impressive technological advances have been reached in the last years, such as the first quantum communication between ground and satellites, as well as the first proof-of-principle experiments in quantum sensing. The development of microwave quantum technologies turned out, nonetheless, to be more challenging. Here, we will discuss the challenges regarding the use of microwaves for quantum communication and sensing. Based on this analysis, we propose a roadmap to achieve real-life applications in these fields. |

Capela, M; Sanz, M; Solano, E; Céleri, L C Kolmogorov-Sinai entropy and dissipation in driven classical Hamiltonian systems Journal Article Physical Review E, 98 (5), pp. 052109, 2018, ISSN: 2470-0053. @article{Capela2018, title = {Kolmogorov-Sinai entropy and dissipation in driven classical Hamiltonian systems}, author = {M Capela and M Sanz and E Solano and L C Céleri}, doi = {10.1103/PhysRevE.98.052109}, issn = {2470-0053}, year = {2018}, date = {2018-01-01}, journal = {Physical Review E}, volume = {98}, number = {5}, pages = {052109}, publisher = {American Physical Society}, abstract = {A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle of maximum entropy allows to establish the connection between entropy in statistical mechanics and information entropy. In this sense, the dissipated energy in a classical Hamiltonian process, known as the thermodynamic entropy production, is connected to the relative entropy between the forward and backward probability densities. Recently, it was revealed that energetic inefficiency and model inefficiency, defined as the difference in mutual information that the system state shares with the future and past environmental variables, are equivalent concepts in Markovian processes. As a consequence, the question about a possible connection between model unpredictability and energetic inefficiency in the framework of classical physics emerges. Here, we address this question by connecting the concepts of random behavior of a classical Hamiltonian system, the Kolmogorov-Sinai entropy, with its energetic inefficiency, the dissipated work. This approach allows us to provide meaningful interpretations of information concepts in terms of thermodynamic quantities.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle of maximum entropy allows to establish the connection between entropy in statistical mechanics and information entropy. In this sense, the dissipated energy in a classical Hamiltonian process, known as the thermodynamic entropy production, is connected to the relative entropy between the forward and backward probability densities. Recently, it was revealed that energetic inefficiency and model inefficiency, defined as the difference in mutual information that the system state shares with the future and past environmental variables, are equivalent concepts in Markovian processes. As a consequence, the question about a possible connection between model unpredictability and energetic inefficiency in the framework of classical physics emerges. Here, we address this question by connecting the concepts of random behavior of a classical Hamiltonian system, the Kolmogorov-Sinai entropy, with its energetic inefficiency, the dissipated work. This approach allows us to provide meaningful interpretations of information concepts in terms of thermodynamic quantities. |