Efficient Quantum Algorithms for Quantum Optimal Control

• URL: http://arxiv.org/abs/2304.02613v2
• Date: Fri, 29 Sep 2023 14:00:54 GMT
• Title: Efficient Quantum Algorithms for Quantum Optimal Control
• Authors: Xiantao Li, Chunhao Wang
• Abstract summary: We present efficient quantum algorithms for solving the quantum optimal control problem. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. Our quantum algorithms require fault-tolerant quantum computers.
• Score: 2.9370710299422607
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr\"odinger 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 Schr\"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

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