Computing complexity measures for quantum states based on exponential families

TL;DR

This paper introduces a method to quantify the complexity of quantum states by measuring their distance from exponential families of thermal states with limited particle interactions, using symmetry-based optimization and algorithms.

Contribution

It develops an algorithm to compute quantum state complexity measures based on exponential family approximations, exploiting symmetries to simplify the optimization process.

Findings

Algorithm effectively computes complexity measures for quantum states.

Symmetry exploitation reduces computational complexity.

Demonstrated applicability on specific quantum examples.

Abstract

Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applicability.