On physical problems that are slightly more difficult than QMA

TL;DR

This paper introduces new complexity classes to better understand the difficulty of quantum physics problems that are slightly harder than QMA, providing a framework to analyze their computational complexity.

Contribution

The authors define new complexity classes based on limited QMA oracle queries and apply them to analyze the complexity of natural quantum physics problems.

Findings

Spectral gap estimation is shown to be harder than QMA.

New complexity classes capture problems slightly beyond QMA.

Framework helps quantify the complexity of quantum physical problems.

Abstract

We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We introduce new complexity classes consisting of problems that are solvable with a small number of queries to a QMA oracle and use these complexity classes to quantify the complexity of several natural computational problems (for example, the complexity of estimating the spectral gap of a Hamiltonian).