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Efficient Optimal Control of Open Quantum Systems

Authors Wenhao He, Tongyang Li , Xiantao Li , Zecheng Li, Chunhao Wang, Ke Wang

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Author Details

Wenhao He
  • Center for Computational Science and Engineering, MIT, Cambridge, MA, USA
  • School of Physics, Peking University, Beijing, China
Tongyang Li
  • Center on Frontiers of Computing Studies, School of Computer Science, Peking University, Beijing, China
Xiantao Li
  • Department of Mathematics, Pennsylvania State University, University Park, PA, USA
Zecheng Li
  • Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, USA
Chunhao Wang
  • Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, USA
Ke Wang
  • Department of Mathematics, Pennsylvania State University, University Park, PA, USA

Funding

  • Li, Tongyang: National Natural Science Foundation of China (Grant Numbers 62372006 and 92365117); The Fundamental Research Funds for the Central Universities, Peking University.
  • Li, Xiantao: NSF DMS-2111221 and CCF-2312456
  • Li, Zecheng: NSF CCF-2312456
  • Wang, Chunhao: NSF CCF-2312456
  • Wang, Ke: NSF DMS-2111221

Acknowledgements

We thank the anonymous reviewers for the valuable feedback.

Cite AsGet BibTex

Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, and Ke Wang. Efficient Optimal Control of Open Quantum Systems. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.TQC.2024.3

Abstract

The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation algorithm for time-dependent Lindbladians with an 𝓁₁-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum algorithm
  • quantum optimal control
  • Lindbladian simulation
  • accelerated gradient descent

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