Quantum algorithms for spin models and simulable gate sets for quantum computation

TL;DR

This paper introduces a framework connecting classical lattice models with quantum circuits, enabling the creation of efficiently simulable quantum gate sets and algorithms for approximating partition functions, with implications for quantum computational complexity.

Contribution

It provides a systematic method to derive quantum algorithms from classical models and generalizes known simulability results, linking classical solvability to quantum computational complexity.

Findings

General framework for mapping classical models to quantum circuits

Efficient quantum algorithms for partition functions of specific models

Simulating these quantum algorithms is BQP-complete

Abstract

We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we recover and generalize the simulability of Valiant's match-gates by invoking the solvability of the free-fermion eight-vertex model. Our mappings furthermore provide a systematic formalism to obtain simple quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. For example, we present an efficient quantum algorithm for the six-vertex model as well as a 2D Ising-type model. We finally show that simulating our quantum algorithms on a classical computer is as hard as simulating universal quantum computation (i.e. BQP-complete).