- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Machine learning assisted zero-area pulse design in an open quantum system

Yi-Ye Li1, Lian-Ao Wu2,3,4, and Zhao-Ming Wang1,5,6,*

  • 1College of Physics and Optoelectronic Engineering, Ocean University of China, Qingdao 266100, China
  • 2Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
  • 3IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
  • 4EHU Quantum Center, University of the Basque Country UPV/EHU, Leioa, 48940 Biscay, Spain
  • 5Engineering Research Center of Advanced Marine Physical Instruments and Equipment of Ministry of Education, Qingdao 266100, China
  • 6Qingdao Key Laboratory of Optics and Optoelectronics, Qingdao 266100, China

  • *Contact author: wangzhaoming@ouc.edu.cn
PDF

Phys. Rev. Research 7, 033191 – Published 25 August, 2025

DOI: https://doi.org/10.1103/11lg-bqbm

Abstract

Accurate and precise quantum control is crucial for quantum information processing. Zero-area pulse control, originally developed for closed systems, has played a significant role in driving quantum systems toward desired states. However, its effectiveness is often compromised by environmental noise. Traditional methods can find optimal pulses for fixed environmental parameters, and they need to be recalculated again once the environmental parameters change. Here, we propose a supervised learning (SL)-based protocol to design optimal zero-area pulses in noisy environments. By including environmental parameters as input during training, the neural network (NN) learns to generate effective controls for various environmental parameters. We demonstrate the protocol using quantum state transmission through a spin chain governed by a non-Markovian master equation. The SL-optimized pulses significantly enhance transmission fidelity compared to ideal pulses, with greater improvements observed at higher system-bath coupling and temperature, where more optimization space exists. Interestingly, fidelity first increases and then decreases with stronger Markovianity, suggesting that highly Markovian environments limit control performance. We also compare the SL method with a genetic algorithm, and the similar results confirm the accuracy and generalization ability of the NN-based approach.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses, Nature (London) 456, 218 (2008).
  2. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).
  3. D. Vitali and P. Tombesi, Using parity kicks for decoherence control, Phys. Rev. A 59, 4178 (1999).
  4. L.-A. Wu, M. S. Byrd, and D. A. Lidar, Efficient universal leakage elimination for physical and encoded qubits, Phys. Rev. Lett. 89, 127901 (2002).
  5. Z.-M. Wang, M. S. Sarandy, and L.-A. Wu, Almost exact state transfer in a spin chain via pulse control, Phys. Rev. A 102, 022601 (2020).
  6. L.-A. Wu, G. Kurizki, and P. Brumer, Master equation and control of an open quantum system with leakage, Phys. Rev. Lett. 102, 080405 (2009).
  7. P. V. Pyshkin, D.-W. Luo, J. Jing, J. Q. You, and L.-A. Wu, Expedited holonomic quantum computation via net zero-energy-cost control in decoherence-free subspace, Sci. Rep. 6, 37781 (2016).
  8. Z.-M. Wang, F.-H. Ren, D.-W. Luo, Z.-Y. Yan, and L.-A. Wu, Almost-exact state transfer by leakage-elimination-operator control in a non-Markovian environment, Phys. Rev. A 102, 042406 (2020).
  9. R.-H. He, R. Wang, F.-H. Ren, L.-C. Zhang, and Z.-M. Wang, Adiabatic speedup in cutting a spin chain via zero-area pulse control, Phys. Rev. A 103, 052606 (2021).
  10. X. Chen, R. Mereau, and D. L. Feder, Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities, Phys. Rev. A 93, 012343 (2016).
  11. L. Diósi and W. T. Strunz, The non-Markovian stochastic Schrödinger equation for open systems, Phys. Lett. A 235, 569 (1997).
  12. T. Yu, Non-Markovian quantum trajectories versus master equations: Finite-temperature heat bath, Phys. Rev. A 69, 062107 (2004).
  13. W. Shi, X. Zhao, and T. Yu, Non-Markovian fermionic stochastic Schrödinger equation for open system dynamics, Phys. Rev. A 87, 052127 (2013).
  14. L. Diósi, N. Gisin, and W. T. Strunz, Non-Markovian quantum state diffusion, Phys. Rev. A 58, 1699 (1998).
  15. Y.-Y. Xie, F.-H. Ren, A. Ablimit, X.-H. Liang, and Z.-M. Wang, Optimized control for high-fidelity state transmission in open systems, Phys. Rev. A 108, 032401 (2023).
  16. Z.-M. Wang, D.-W. Luo, M. S. Byrd, L.-A. Wu, T. Yu, and B. Shao, Adiabatic speedup in a non-Markovian quantum open system, Phys. Rev. A 98, 062118 (2018).
  17. F. Albarelli, U. Shackerley-Bennett, and A. Serafini, Locally optimal control of continuous-variable entanglement, Phys. Rev. A 98, 062312 (2018).
  18. S.-S. Nie, F.-H. Ren, R.-H. He, J. Wu, and Z.-M. Wang, Control cost and quantum speed limit time in controlled almost-exact state transmission in open systems, Phys. Rev. A 104, 052424 (2021).
  19. M. Y. Niu, S. Boixo, V. N. Smelyanskiy, and H. Neven, Universal quantum control through deep reinforcement learning, npj Quantum Inf. 5, 33 (2019).
  20. D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980.
  21. L. Mortimer, M. P. Estarellas, T. P. Spiller, and I. D’Amico, Evolutionary computation for adaptive quantum device design, Adv. Quantum Technol. 4, 2100013 (2021).
  22. Y.-Y. Xie, F.-H. Ren, R.-H. He, A. Ablimit, and Z.-M. Wang, Stochastic learning control of adiabatic speedup in a non-Markovian open qutrit system, Phys. Rev. A 106, 062612 (2022).
  23. R.-H. He, R. Wang, S.-S. Nie, J. Wu, J.-H. Zhang, and Z.-M. Wang, Deep reinforcement learning for universal quantum state preparation via dynamic pulse control, EPJ Quantum Technol. 8, 29 (2021).
  24. C.-C. Li, R.-H. He, and Z.-M. Wang, Enhanced quantum state preparation via stochastic predictions of neural networks, Phys. Rev. A 108, 052418 (2023).
  25. Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015).
  26. Z.-M. Wang and T.-Z. Chen, Adaptive denoising quantum state preparation in a dynamic environment, Phys. Rev. Res. 6, 043195 (2024).
  27. S. Bose, Quantum communication through an unmodulated spin chain, Phys. Rev. Lett. 91, 207901 (2003).
  28. M. Christandl, N. Datta, A. Ekert, and A. J. Landahl, Perfect state transfer in quantum spin networks, Phys. Rev. Lett. 92, 187902 (2004).
  29. M. Christandl, N. Datta, T. C. Dorlas, A. Ekert, A. Kay, and A. J. Landahl, Perfect transfer of arbitrary states in quantum spin networks, Phys. Rev. A 71, 032312 (2005).
  30. A. Ablimit, R.-H. He, Y.-Y. Xie, L.-A. Wu, and Z.-M. Wang, Quantum energy current induced coherence in a spin chain under non-Markovian environments, Entropy 24, 1406 (2022).
  31. Z.-M. Wang, F.-H. Ren, D.-W. Luo, Z.-Y. Yan, and L.-A. Wu, Quantum state transmission through a spin chain in finite-temperature heat baths, J. Phys. A: Math. Theor. 54, 155303 (2021).
  32. H. Wang and M. Thoss, From coherent motion to localization: II. Dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature, Chem. Phys. 370, 78 (2010).
  33. G. Ritschel and A. Eisfeld, Analytic representations of bath correlation functions for Ohmic and super-Ohmic spectral densities using simple poles, J. Chem. Phys. 141, 094101 (2014).
  34. C. Meier and D. J. Tannor, Non-Markovian evolution of the density operator in the presence of strong laser fields, J. Chem. Phys. 111, 3365 (1999).
  35. A. Ishizaki and G. R. Fleming, Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: Reduced hierarchy equation approach, J. Chem. Phys. 130, 234111 (2009).
  36. G. Mouloudakis, T. Ilias, and P. Lambropoulos, Arbitrary-length XX spin chains boundary-driven by non-Markovian environments, Phys. Rev. A 105, 012429 (2022).
  37. M. L. Hu and H. L. Lian, State transfer in intrinsic decoherence spin channels, Eur. Phys. J. D 55, 711 (2009).
  38. Z.-M. Wang, M. S. Byrd, J. Jing, and L.-A. Wu, Adiabatic leakage elimination operator in an experimental framework, Phys. Rev. A 97, 062312 (2018).
  39. J.-S. Tai, K.-T. Lin, and H.-S. Goan, Optimal control of quantum gates in an exactly solvable non-Markovian open quantum bit system, Phys. Rev. A 89, 062310 (2014).
  40. S. Zheng, Q. He, M. S. Byrd, and L.-A. Wu, Nonperturbative leakage elimination for a logical qubit encoded in a mechanical oscillator, Phys. Rev. Res. 2, 033378 (2020).

Outline

Information

Phys. Rev. Research 7, 033191– Published 25 August, 2025
  • Received 16 April 2025
  • Accepted 8 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation