Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits

TL;DR

This paper introduces a kernel-based method using classical shadows to efficiently learn linear properties of large-qubit quantum circuits, balancing prediction accuracy and computational cost, with validation up to 60 qubits.

Contribution

It demonstrates a scalable approach for learning linear properties of quantum circuits using classical shadows and trigonometric expansions, addressing complexity challenges.

Findings

Sample complexity scales linearly with the number of tunable gates

Proposed method achieves controllable trade-off between accuracy and computation

Validated on simulations with up to 60 qubits

Abstract

The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial question: can linear properties of a large-qubit circuit with d tunable RZ gates and G-d Clifford gates be efficiently learned from measurement data generated by varying classical inputs? In this work, we prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. To address this challenge, we propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead. Our results advance two crucial realms in quantum computation: the exploration of quantum algorithms with practical utilities and learning-based quantum system certification. We conduct numerical simulations to validate our proposals across diverse scenarios, encompassing quantum information processing protocols, Hamiltonian simulation, and variational quantum algorithms up to 60 qubits.