Simulation of Classical Thermal States on a Quantum Computer: A Transfer Matrix Approach

TL;DR

This paper introduces a hybrid quantum-classical algorithm for efficiently simulating thermal states of classical Hamiltonians on quantum computers, with advantages over existing methods especially for 2D Ising models.

Contribution

The authors develop a new transfer matrix-based approach that reduces computational overhead and provides exponential speedup for certain 2D classical models.

Findings

Efficient simulation of specific classical models on quantum computers.

Exponential advantage for 2D Ising models with magnetic field.

Avoids exponential overheads of previous quantum algorithms.

Abstract

We present a hybrid quantum-classical algorithm to simulate thermal states of a classical Hamiltonians on a quantum computer. Our scheme employs a sequence of locally controlled rotations, building up the desired state by adding qubits one at a time. We identify a class of classical models for which our method is efficient and avoids potential exponential overheads encountered by Grover-like or quantum Metropolis schemes. Our algorithm also gives an exponential advantage for 2D Ising models with magnetic field on a square lattice, compared with the previously known Zalka's algorithm.