Time-Optimal Quantum Driving by Variational Circuit Learning

TL;DR

This paper introduces a hybrid quantum-classical approach using variational circuit learning to achieve time-optimal quantum control, demonstrating its effectiveness in simulating quantum dynamics and exploring quantum speed limits.

Contribution

It presents a novel method combining digital quantum simulation with variational circuit learning for optimal quantum control, addressing robustness and barren plateau issues.

Findings

Successful simulation of wave-packet expansion on quantum hardware

Identification of the connection between control phase transition and quantum speed limit

Method shows robustness against errors and lacks barren plateaus

Abstract

The simulation of quantum dynamics on a digital quantum computer with parameterized circuits has widespread applications in fundamental and applied physics and chemistry. In this context, using the hybrid quantum-classical algorithm, combining classical optimizers and quantum computers, is a competitive strategy for solving specific problems. We put forward its use for optimal quantum control. We simulate the wave-packet expansion of a trapped quantum particle on a quantum device with a finite number of qubits. We then use circuit learning based on gradient descent to work out the intrinsic connection between the control phase transition and the quantum speed limit imposed by unitary dynamics. We further discuss the robustness of our method against errors and demonstrate the absence of barren plateaus in the circuit. The combination of digital quantum simulation and hybrid circuit learning opens up new prospects for quantum optimal control.