Quantum simulation of classical thermal states

TL;DR

This paper demonstrates a universal quantum Hamiltonian framework that encodes classical thermal states as ground states of local quantum systems, enabling quantum simulation of classical statistical mechanics.

Contribution

It introduces a universal 5-body local quantum Hamiltonian that maps classical thermal states to quantum ground states across all dimensions and models.

Findings

Quantum states correspond to classical thermal states

Universal 5-body Hamiltonian encodes all classical models

Adjustable parameters simulate different temperatures and interactions

Abstract

We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum state such that the reduced density operator behaves as the thermal state of the classical system. We show that all these quantum states are unique ground states of a universal 5-body local quantum Hamiltonian acting on a (polynomially enlarged) system of qubits arranged on a 2D lattice. The only free parameters of the quantum Hamiltonian are coupling strengthes of two-body interactions, which allow one to choose the type and dimension of the classical model as well as the interaction strength and temperature.