Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
This addresses the challenge of certifying and analyzing quantum systems for quantum computing researchers, offering a method to balance efficiency and accuracy in learning tasks.
The paper tackles the problem of efficiently learning linear properties of bounded-gate quantum circuits from measurement data, proving that sample complexity scales linearly with the number of tunable gates while computational complexity can be exponential, and proposes a kernel-based method to trade off accuracy and computational cost, validated in simulations up to 60 qubits.
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.