Hamiltonian Learning and Certification Using Quantum Resources

TL;DR

This paper presents an efficient algorithm for certifying the correctness of quantum simulators by inferring their Hamiltonians using trusted quantum resources, enabling validation of large-scale analog quantum simulations.

Contribution

It introduces a novel method for Hamiltonian learning and certification that leverages quantum resources, addressing a key challenge in validating analog quantum simulators.

Findings

Successfully infers Hamiltonians for large frustrated Ising models

Demonstrates quantum resources make certification computationally feasible

Provides an algorithm applicable under weak assumptions

Abstract

In recent years quantum simulation has made great strides culminating in experiments that operate in a regime that existing supercomputers cannot easily simulate. Although this raises the possibility that special purpose analog quantum simulators may be able to perform computational tasks that existing computers cannot, it also introduces a major challenge: certifying that the quantum simulator is in fact simulating the correct quantum dynamics. We provide an algorithm that, under relatively weak assumptions, can be used to efficiently infer the Hamiltonian of a large but untrusted quantum simulator using a trusted quantum simulator. We illustrate the power of this approach by showing numerically that it can inexpensively learn the Hamiltonians for large frustrated Ising models, demonstrating that quantum resources can make certifying analog quantum simulators tractable.