Efficient Quantum Algorithms for Quantum Optimal Control

Xiantao Li, Chunhao Wang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:19982-19994, 2023.

Abstract

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schrödinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schrödinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-li23ab, title = {Efficient Quantum Algorithms for Quantum Optimal Control}, author = {Li, Xiantao and Wang, Chunhao}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {19982--19994}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/li23ab/li23ab.pdf}, url = {https://proceedings.mlr.press/v202/li23ab.html}, abstract = {In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schrödinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schrödinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.} }
Endnote
%0 Conference Paper %T Efficient Quantum Algorithms for Quantum Optimal Control %A Xiantao Li %A Chunhao Wang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-li23ab %I PMLR %P 19982--19994 %U https://proceedings.mlr.press/v202/li23ab.html %V 202 %X In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schrödinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schrödinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.
APA
Li, X. & Wang, C.. (2023). Efficient Quantum Algorithms for Quantum Optimal Control. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:19982-19994 Available from https://proceedings.mlr.press/v202/li23ab.html.

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