Model-Free Quantum Control with Reinforcement Learning
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A machine-learning agent learns how to control a quantum system---a key element of any quantum technology without any prior knowledge---by studying how a real quantum system responds to various actions.
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The optimized GKP ququart achieved beyond break-even error correction with a gain of 1.87 ± 0.03.
“Using a reinforcement learning agent21,22, we optimized the Gottesman–Kitaev–Preskill qutrit (ququart) as a ternary (quaternary) quantum memory and achieved beyond break-even error correction with a gain of 1.82 ± 0.03 (1.87 ± 0.03).”
From Quantum error correction of qudits beyond break-even (2025) · cites this paper as [21]
Section B, “Preparation of stabilizer states” (page unavailable), describes training a reinforcement-learning agent to prepare a GKP grid state. It does not report an optimized GKP ququart memory, beyond break-even error correction, or a gain of 1.87 ± 0.03. (LLM, conf=0.86)
Experimental — accuracy not yet measuredThe optimized GKP qutrit achieved beyond break-even error correction with a gain of 1.82 ± 0.03.
“Using a reinforcement learning agent21,22, we optimized the Gottesman–Kitaev–Preskill qutrit (ququart) as a ternary (quaternary) quantum memory and achieved beyond break-even error correction with a gain of 1.82 ± 0.03 (1.87 ± 0.03).”
From Quantum error correction of qudits beyond break-even (2025) · cites this paper as [21]
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SciPy 1.0: fundamental algorithms for scientific computing in Python
Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. (2020) · Nature Methods · doi:10.1038/s41592-019-0686-2 · Cited by 38,430 · see citing works
Quantum Computation and Quantum Information: 10th Anniversary Edition
Nielsen, M. A., & Chuang, I. L. (2012) · doi:10.1017/cbo9780511976667 · Cited by 8,436 · see citing works
Greff, K., Srivastava, R. K., Koutnik, J., Steunebrink, B. R., & Schmidhuber, J. (2017) · IEEE Transactions on Neural Networks and Learning Systems · doi:10.1109/tnnls.2016.2582924 · Cited by 6,955 · see citing works
A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play
Silver, D., Hubert, T., Schrittwieser, J., Antonoglou, I., Lai, M., Guez, A., Lanctot, M., Sifre, L., Kumaran, D., Graepel, T., et al. (2018) · Science · doi:10.1126/science.aar6404 · Cited by 3,562 · cited 2× · see citing works
“We expect that in the limit of infinite averaging, the training would proceed as if the fidelity F was directly available to be used as a reward (blue line).”
Variational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385 · cited 1× · see citing works
“We refer to the literature on variational quantum algorithms for more details [104].”
Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T., & Glaser, S. J. (2005) · Journal of Magnetic Resonance · doi:10.1016/j.jmr.2004.11.004 · Cited by 1,854 · see citing works
An introduction to deep reinforcement learning
François-Lavet, V., Henderson, P., Islam, R., Bellemare, M. G., & Pineau, J. (2018) · doi:10.1561/9781680835397 · Cited by 544 · see citing works
Direct Fidelity Estimation from Few Pauli Measurements
Flammia, S. T., & Liu, Y.-K. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.230501 · Cited by 449 · see citing works
Encoding a qubit in a trapped-ion mechanical oscillator
Flühmann, C., Nguyen, T. L., Marinelli, M., Negnevitsky, V., Mehta, K., & Home, J. P. (2019) · Nature · doi:10.1038/s41586-019-0960-6 · Cited by 394 · see citing works
Experimental phase estimation enhanced by machine learning
Lumino, A., Polino, E., Rab, A. S., Milani, G., Spagnolo, N., Wiebe, N., & Sciarrino, F. (2018) · Physical Review Applied · doi:10.1103/physrevapplied.10.044033 · Cited by 97 · see citing works
Flagged first, then by citations
Research works printed but not linked: 95
- T. Caneva, T. Calarco, and S. Montangero, Chopped Random-Basis Quantum Optimization, Phys. Rev. A 84, 022326 (2011). · DOI
- P. De Fouquieres, S. G. Schirmer, S. J. Glaser, and I. Kuprov, Second Order Gradient Ascent Pulse Engineer- ing, J. Magn. Reson. 212, 412 (2011). · DOI
- N. Leung, M. Abdelhafez, J. Koch, and D. Schuster, Speedup for Quantum Optimal Control from Automatic Differentiation Based on Graphics Processing Units, Phys. Rev. A 95, 042318 (2017). · DOI
- M. Abdelhafez, D. I. Schuster, and J. Koch, Gradient- Based Optimal Control of Open Quantum Systems Using Quantum Trajectories and Automatic Differentiation, Phys. Rev. A 99, 052327 (2019). · DOI
- J. Kelly, R. Barends, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, I. C. Hoi, E. Jeffrey et al., Optimal Quantum Control Using Randomized Benchmarking, Phys. Rev. Lett. 112, 240504 (2014). · DOI
- Z. Chen, J. Kelly, C. Quintana, R. Barends, B. Campbell, Y. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Lucero et al., Measuring and Suppressing Quantum State Leakage in a Superconducting Qubit, Phys. Rev. Lett. 116, 020501 (2016). · DOI
- M. A. Rol, C. C. Bultink, T. E. O'Brien, S. R. de Jong, L. S. Theis, X. Fu, F. Luthi, R. F. L. Vermeulen, J. C. de Sterke, A. Bruno et al., Restless Tuneup of High-Fidelity Qubit Gates, Phys. Rev. Applied 7, 041001(R) (2017). · DOI
- M. Werninghaus, D. J. Egger, F. Roy, S. Machnes, F. K. Wilhelm, and S. Filipp, Leakage Reduction in Fast Super- conducting Qubit Gates via Optimal Control, npj Quantum Inf. 7, 14 (2021). · DOI
- R. S. Judson and H. Rabitz, Teaching Lasers to Control Molecules, Phys. Rev. Lett. 68, 1500 (1992). · DOI
- D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot et al., Mastering the Game of Go with Deep Neural Networks and Tree Search, Nature (London) 529, 484 (2016). · DOI · Paper page
- V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski et al., Human-Level Control through Deep Reinforcement Learning, Nature (London) 518, 529 (2015). · DOI · Paper page
- O. Vinyals, I. Babuschkin, W. M. Czarnecki, M. Mathieu, A. Dudzik, J. Chung, D. H. Choi, R. Powell, T. Ewalds, P. Georgiev et al., Grandmaster Level in StarCraft II Using Multi-Agent Reinforcement Learning, Nature (London) 575, 350 (2019). · DOI · Paper page
- S. Levine, C. Finn, T. Darrell, and P. Abbeel, End-to-End Training of Deep Visuomotor Policies, J. Mach. Learn. Research 17, 1 (2015), https://www.jmlr.org/papers/ volume17/15-522/15-522.pdf.
- T. Haarnoja, S. Ha, A. Zhou, J. Tan, G. Tucker, and S. Levine, Learning to Walk via Deep Reinforcement Learn- ing, Proceedings of Robotics: Science and Systems (2019), 10.15607/RSS.2019.XV.011. · DOI · Paper page
- C. Chen, D. Dong, H. X. Li, J. Chu, and T. J. Tarn, Fidelity-Based Probabilistic Q-Learning for Control of Quantum Systems, IEEE Trans. Neural Netw. Learn. Syst. 25, 920 (2014). · DOI
- M. Bukov, A. Day, D. Sels, P. Weinberg, A. Polkovnikov, and P. Mehta, Reinforcement Learning in Different Phases of Quantum Control, Phys. Rev. X 8, 031086 (2018). · DOI
- M. Bukov, Reinforcement Learning for Autonomous Preparation of Floquet-Engineered States: Inverting the Quantum Kapitza Oscillator, Phys. Rev. B 98, 224305 (2018). · DOI
- X.-M. Zhang, Z. Wei, R. Asad, X.-C. Yang, and X. Wang, When Does Reinforcement Learning Stand out in Quantum Control? A Comparative Study on State Preparation, npj Quantum Inf. 5, 85 (2019). · DOI
- R. Porotti, D. Tamascelli, M. Restelli, and E. Prati, Coherent Transport of Quantum States by Deep Reinforce- ment Learning, Commun. Phys. 2, 61 (2019). · DOI
- Z. An, H.-J. Song, Q.-K. He, and D. L. Zhou, Quantum Optimal Control of Multilevel Dissipative Quantum Sys- tems with Reinforcement Learning, Phys. Rev. A 103, 012404 (2021). · DOI
- M. August and J. M. Hernández-Lobato, in Lecture Notes in Computer Science (2018), Vol. 11203, pp. 591-613, 10.1007/978-3-030-02465-9_43. · DOI
- T. Haug, W.-K. Mok, J.-B. You, W. Zhang, C. E. Png, and L.-C. Kwek, Classifying Global State Preparation via Deep Reinforcement Learning, Mach. Learn. 2, 01LT02 (2021). · DOI
- E.-J. Kuo, Y.-L. L. Fang, and S. Y.-C. Chen, Quantum Architecture Search via Deep Reinforcement Learning, arXiv:2104.07715. · arXiv
- Z. T. Wang, Y. Ashida, and M. Ueda, Deep Reinforcement Learning Control of Quantum Cartpoles, Phys. Rev. Lett. 125, 100401 (2020). · DOI
- S. Borah, B. Sarma, M. Kewming, G. J. Milburn, and J. Twamley, Measurement Based Feedback Quantum Con- trol with Deep Reinforcement Learning, Phys. Rev. Lett. 127, 190403 (2021). · DOI
- M. Dalgaard, F. Motzoi, J. J. Sørensen, and J. Sherson, Global Optimization of Quantum Dynamics with Alpha- Zero Deep Exploration, npj Quantum Inf. 6, 6 (2020). · DOI
- M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven, Universal Quantum Control through Deep Reinforcement Learning, npj Quantum Inf. 5, 33 (2019). · DOI
- Z. An and D. L. Zhou, Deep Reinforcement Learning for Quantum Gate Control, Europhys. Lett. 126, 60002 (2019). · DOI
- T. Fösel, P. Tighineanu, T. Weiss, and F. Marquardt, Reinforcement Learning with Neural Networks for Quan- tum Feedback, Phys. Rev. X 8, 031084 (2018). · DOI
- P. Andreasson, J. Johansson, S. Liljestrand, and M. Granath, Quantum Error Correction for the Toric Code Using Deep Reinforcement Learning, Quantum 3, 183 (2019). · DOI
- H. P. Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis, Optimizing Quantum Error Correction Codes with Reinforcement Learning, Quantum 3, 215 (2019). · DOI
- L. D. Colomer, M. Skotiniotis, and R. Muñoz-Tapia, Reinforcement Learning for Optimal Error Correction of Toric Codes, Phys. Lett. A 384, 126353 (2020). · DOI
- H. Xu, J. Li, L. Liu, Y. Wang, H. Yuan, and X. Wang, Generalizable Control for Quantum Parameter Estimation through Reinforcement Learning, npj Quantum Inf. 5, 82 (2019). · DOI
- J. Schuff, L. J. Fiderer, and D. Braun, Improving the Dynamics of Quantum Sensors with Reinforcement Learn- ing, New J. Phys. 22, 035001 (2020). · DOI
- Y. Baum, M. Amico, S. Howell, M. Hush, M. Liuzzi, P. Mundada, T. Merkh, A. R. Carvalho, and M. J. Biercuk, Experimental Deep Reinforcement Learning for Error- Robust Gate-Set Design on a Superconducting Quantum Computer, PRX Quantum 2, 040324 (2021). · DOI
- J. Barry, D. T. Barry, and S. Aaronson, Quantum Partially Observable Markov Decision Processes, Phys. Rev. A 90, 032311 (2014). · DOI
- D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum Dynamics of Single Trapped Ions, Rev. Mod. Phys. 75, 281 (2003). · DOI · Paper page
- C. D. Bruzewicz, J. Chiaverini, R. McConnell, and J. M. Sage, Trapped-Ion Quantum Computing: Progress and Challenges, Appl. Phys. Rev. 6, 021314 (2019). · DOI · Paper page
- P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gustavsson, and W. D. Oliver, A Quantum Engineer's Guide to Superconducting Qubits, Appl. Phys. Rev. 6, 021318 (2019). · DOI
- A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit Quantum Electrodynamics, Rev. Mod. Phys. 93, 025005 (2021). · DOI
- N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang et al., Extending the Lifetime of a Quantum Bit with Error Correction in Superconducting Circuits, Nature (London) 536, 441 (2016). · DOI · Paper page
- P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys- Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf et al., Quantum Error Correc- tion of a Qubit Encoded in Grid States of an Oscillator, Nature (London) 584, 368 (2020). · DOI · Paper page
- L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C.-L. Zou et al., Quantum Error Correction and Universal Gate Set Operation on a Binomial Bosonic Logical Qubit, Nat. Phys. 15, 503 (2019). · DOI
- W. Wang, Y. Wu, Y. Ma, W. Cai, L. Hu, X. Mu, Y. Xu, Z.-J. Chen, H. Wang, Y. P. Song et al., Heisenberg-Limited Single-Mode Quantum Metrology in a Superconducting Circuit, Nat. Commun. 10, 4382 (2019). · DOI
- R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator, Nat. Commun. 8, 94 (2017). · DOI
- A. Eickbusch, V. Sivak, A. Z. Ding, S. S. Elder, S. R. Jha, J. Venkatraman, B. Royer, S. M. Girvin, R. J. Schoelkopf, and M. H. Devoret, Fast Universal Control of an Oscil- lator with Weak Dispersive Coupling to a Qubit, arXiv:2111.06414. · arXiv
- M. Kudra, M. Kervinen, I. Strandberg, S. Ahmed, M. Scigliuzzo, A. Osman, D. P. Lozano, G. Ferrini, J. Bylander, A. F. Kockum et al., Robust Preparation of Wigner- Negative States with Optimized SNAP-Displacement Se- quences, arXiv:2111.07965. · arXiv
- C. Flühmann and J. P. Home, Direct Characteristic-Func- tion Tomography of Quantum States of the Trapped- Ion Motional Oscillator, Phys. Rev. Lett. 125, 043602 (2020). · DOI
- D. Gottesman, A. Kitaev, and J. Preskill, Encoding a Qubit in an Oscillator, Phys. Rev. A 64, 012310 (2001). · DOI · Paper page
- M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New Class of Quantum Error-Correcting Codes for a Bosonic Mode, Phys. Rev. X 6, 031006 (2016). · DOI
- A. Garcia-Saez and J. Riu, Quantum Observables for continuous control of the Quantum Approximate Optimi- zation Algorithm via Reinforcement Learning, arXiv: 1911.09682. · arXiv
- M. M. Wauters, E. Panizon, G. B. Mbeng, and G. E. Santoro, Reinforcement-Learning-Assisted Quantum Opti- mization, Phys. Rev. Research 2, 033446 (2020). · DOI · Paper page
- M. Bilkis, M. Rosati, R. M. Yepes, and J. Calsamiglia, Real-Time Calibration of Coherent-State Receivers: Learning by Trial and Error, Phys. Rev. Research 2, 033295 (2020). · DOI
- S. Russel and P. Norvig, Artificial Intelligence: A Modern Approach, 4th ed. (Pearson, 2020), https://www.amazon .com/Artificial-Intelligence-A-Modern-Approach/dp/ 0134610997.
- J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-Insensitive Qubit Design Derived from the Cooper Pair Box, Phys. Rev. A 76, 042319 (2007). · DOI · Paper page
- K. Mølmer, Y. Castin, and J. Dalibard, Monte Carlo Wave- Function Method in Quantum Optics, J. Opt. Soc. Am. B 10, 524 (1993). · DOI
- M. Jerger, A. Kulikov, Z. Vasselin, and A. Fedorov, In Situ Characterization of Qubit Control Lines: A Qubit as a Vector Network Analyzer, Phys. Rev. Lett. 123, 150501 (2019). · DOI
- M. A. Rol, L. Ciorciaro, F. K. Malinowski, B. M. Tarasinski, R. E. Sagastizabal, C. C. Bultink, Y. Salathe, N. Haandbaek, J. Sedivy, and L. Dicarlo, Time-Domain Characterization and Correction of On-Chip Distortion of Control Pulses in a Quantum Processor, Appl. Phys. Lett. 116, 054001 (2020). · DOI
- T. Propson, B. E. Jackson, J. Koch, Z. Manchester, and D. I. Schuster, Robust Quantum Optimal Control with Trajectory Optimization, Phys. Rev. Applied 17, 014036 (2022). · DOI
- V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller, Playing Atari with Deep Reinforcement Learning, arXiv:1312.5602. · arXiv
- S. Hochreiter and J. Schmidhuber, Long Short-Term Memory, Neural Comput. 9, 1735 (1997). · DOI · Paper page
- J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, Proximal Policy Optimization Algorithms, arXiv: 1707.06347. · arXiv
- See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevX.12.011059 for introduc- tion to PPO algorithm, implementational details, and list of hyperparameters.
- S. Krastanov, V. V. Albert, C. Shen, C.-L. Zou, R. W. Heeres, B. Vlastakis, R. J. Schoelkopf, and L. Jiang, Universal Control of an Oscillator with Dispersive Cou- pling to a Qubit, Phys. Rev. A 92, 040303(R) (2015). · DOI
- R. W. Heeres, B. Vlastakis, E. Holland, S. Krastanov, V. V. Albert, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Cavity State Manipulation Using Photon-Number Selective Phase Gates, Phys. Rev. Lett. 115, 137002 (2015). · DOI
- P. Reinhold, S. Rosenblum, W.-L. Ma, L. Frunzio, L. Jiang, and R. J. Schoelkopf, Error-Corrected Gates on an Encoded Qubit, Nat. Phys. 16, 822 (2020). · DOI
- W.-L. Ma, M. Zhang, Y. Wong, K. Noh, S. Rosenblum, P. Reinhold, R. J. Schoelkopf, and L. Jiang, Path-Indepen- dent Quantum Gates with Noisy Ancilla, Phys. Rev. Lett. 125, 110503 (2020). · DOI
- T. Fösel, S. Krastanov, F. Marquardt, and L. Jiang, Efficient Cavity Control with SNAP Gates, arXiv:2004.14256. · arXiv
- M. Kliesch and I. Roth, Theory of Quantum System Certification, PRX Quantum 2, 010201 (2021). · DOI
- D. I. Schuster, A. A. Houck, J. A. Schreier, A. Wallraff, J. M. Gambetta, A. Blais, L. Frunzio, J. Majer, B. Johnson, M. H. Devoret et al., Resolving Photon Number States in a Superconducting Circuit, Nature (London) 445, 515 (2007). · DOI
- W. Pfaff, C. J. Axline, L. D. Burkhart, U. Vool, P. Rein- hold, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Controlled Release of Multiphoton Quantum States from a Microwave Cavity Memory, Nat. Phys. 13, 882 (2017). · DOI
- M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard et al., TensorFlow: A System for Large-Scale Machine Learning, arXiv:1605.08695. · arXiv
- M. P. da Silva, O. Landon-Cardinal, and D. Poulin, Practical Characterization of Quantum Devices without Tomography, Phys. Rev. Lett. 107, 210404 (2011). · DOI
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2010).
- K. Duivenvoorden, B. M. Terhal, and D. Weigand, Single- Mode Displacement Sensor, Phys. Rev. A 95, 012305 (2017). · DOI
- K. Noh, S. M. Girvin, and L. Jiang, Encoding an Oscillator into Many Oscillators, Phys. Rev. Lett. 125, 080503 (2020). · DOI
- B. M. Terhal and D. Weigand, Encoding a Qubit into a Cavity Mode in Circuit QED Using Phase Estimation, Phys. Rev. A 93, 012315 (2016). · DOI
- P. Campagne-Ibarcq, A. Eickbusch, S. Touzard, E. Zalys- Geller, N. E. Frattini, V. V. Sivak, P. Reinhold, S. Puri, S. Shankar, R. J. Schoelkopf et al., Quantum Error Correc- tion of a Qubit Encoded in Grid States of an Oscillator, Nature (London) 584, 368 (2020). · DOI · Paper page
- B. Royer, S. Singh, and S. M. Girvin, Stabilization of Finite-Energy Gottesman-Kitaev-Preskill States, Phys. Rev. Lett. 125, 260509 (2020). · DOI · Paper page
- B. de Neeve, T. L. Nguyen, T. Behrle, and J. Home, Error Correction of a Logical Grid State Qubit by Dissipative Pumping (2022) 10.1038/s41567-021-01487-7. · DOI · Paper page
- B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Deterministically Encoding Quantum Information Using 100-Photon Schrodinger Cat States, Science 342, 607 (2013). · DOI
- C. Sayrin, I. Dotsenko, X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune et al., Real-Time Quantum Feedback Prepares and Stabilizes Photon Number States, Nature (London) 477, 73 (2011). · DOI
- C. Shen, K. Noh, V. V. Albert, S. Krastanov, M. H. Devoret, R. J. Schoelkopf, S. M. Girvin, and L. Jiang, Quantum Channel Construction with Circuit Quantum Electrodynamics, Phys. Rev. B 95, 134501 (2017). · DOI
- A. Kenfack and K. Zyczkowski, Negativity of the Wigner Function as an Indicator of Non-classicality, J. Opt. B 6, 396 (2004). · DOI · Paper page
- J. Schulman, P. Moritz, S. Levine, M. Jordan, and P. Abbeel, High-Dimensional Continuous Control Using Generalized Advantage Estimation, arXiv:1506.02438. · arXiv
- Y. Duan, X. Chen, R. Houthooft, J. Schulman, and P. Abbeel, Benchmarking Deep Reinforcement Learning for Continuous Control, 33rd International Conference on Machine Learning 3, 2001 (2016), https://arxiv.org/abs/ 1604.06778.
- A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention Is All You Need, arXiv:1706.03762. · arXiv
- S. Krastanov, S. Zhou, S. T. Flammia, and L. Jiang, Stochastic Estimation of Dynamical Variables, Quantum Sci. Technol. 4, 035003 (2019). · DOI
- S. Krastanov, K. Head-Marsden, S. Zhou, S. T. Flammia, L. Jiang, and P. Narang, Unboxing Quantum Black Box Models: Learning Non-Markovian Dynamics, arXiv: 2009.03902. · arXiv
- E. Flurin, L. S. Martin, S. Hacohen-Gourgy, and I. Siddiqi, Using a Recurrent Neural Network to Reconstruct Quan- tum Dynamics of a Superconducting Qubit from Physical Observations, Phys. Rev. X 10, 011006 (2020). · DOI
- L. Banchi, E. Grant, A. Rocchetto, and S. Severini, Modelling Non-Markovian Quantum Processes with Re- current Neural Networks, New J. Phys. 20, 123030 (2018). · DOI
- A. Plaat, W. Kosters, and M. Preuss, Deep Model-Based Reinforcement Learning for High-Dimensional Problems, A Survey, arXiv:2008.05598. · arXiv
- B. Kneer and C. K. Law, Preparation of Arbitrary En- tangled Quantum States of a Trapped Ion, Phys. Rev. A 57, 2096 (1998). · DOI
- S. Haroche and J.-M. Raimond, Exploring the Quantum (Oxford University Press, New York, 2006).
- M. A. Nielsen, A Simple Formula for the Average Gate Fidelity of a Quantum Dynamical Operation, Phys. Lett. A 303, 249 (2002). · DOI · Paper page
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Self-citation
- Authors
- Sivak, V. V., Eickbusch, A., Liu, H., Royer, B., Tsioutsios, I., & Devoret, M. H.
- Affiliations
- Yale University (US)
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2022-03-28
- Volume
- 12
- Issue
- 1
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W3158332310
- Cited by
- 130
- References
- 10
- Citations by year
- 2026: 22 · 2025: 45 · 2024: 24 · 2023: 25 · 2022: 12 · 2021: 2
- FWCI
- 8.72
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Army Research Office (W911NF-18-1-0212)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Reinforcement Learning in Robotics
- Keywords
- reinforcement learning, quantum control, machine learning agents, quantum systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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