Direct certification of a class of quantum simulations

TL;DR

This paper introduces a non-interactive certification protocol for ground states of certain quantum Hamiltonians, enabling verification of complex quantum simulations that are classically intractable, including those demonstrating quantum supremacy.

Contribution

It develops weak-membership certification methods for ground states, applicable to analog quantum simulations and encodings of universal quantum computation and IQP circuits.

Findings

Protocol efficiently certifies ground states with polynomially bounded error.

Applicable to classically intractable quantum simulations such as Feynman-Kitaev Hamiltonians.

Enables verification of quantum supremacy demonstrations.

Abstract

One of the main challenges in the field of quantum simulation and computation is to identify ways to certify the correct functioning of a device when a classical efficient simulation is not available. Important cases are situations in which one cannot classically calculate local expectation values of state preparations efficiently. In this work, we develop weak-membership formulations of the certification of ground state preparations. We provide a non-interactive protocol for certifying ground states of frustration-free Hamiltonians based on simple energy measurements of local Hamiltonian terms. This certification protocol can be applied to classically intractable analog quantum simulations: For example, using Feynman-Kitaev Hamiltonians, one can encode universal quantum computation in such ground states. Moreover, our certification protocol is applicable to ground states encodings of IQP circuits demonstration of quantum supremacy. These can be certified efficiently when the error is polynomially bounded.