Polynomial-time algorithm for simulation of weakly interacting quantum spin systems

TL;DR

This paper presents a polynomial-time algorithm for approximating the ground state energy and correlations in weakly interacting quantum spin systems, leveraging perturbation theory and a generalized ansatz.

Contribution

It introduces a novel polynomial-time algorithm for simulating weakly interacting quantum spin systems using a perturbative approach and a generalized Kirkwood-Thomas ansatz.

Findings

Algorithm computes ground state energy efficiently for small perturbations.

Works for Hamiltonians with bounded degree interaction graphs.

Performance depends on spectral gap and interaction strength.

Abstract

We describe an algorithm that computes the ground state energy and correlation functions for 2-local Hamiltonians in which interactions between qubits are weak compared to single-qubit terms. The running time of the algorithm is polynomial in the number of qubits and the required precision. Specifically, we consider Hamiltonians of the form $H=H_0+\epsilon V$, where H_0 describes non-interacting qubits, V is a perturbation that involves arbitrary two-qubit interactions on a graph of bounded degree, and $\epsilon$ is a small parameter. The algorithm works if $|\epsilon|$ is below a certain threshold value that depends only upon the spectral gap of H_0, the maximal degree of the graph, and the maximal norm of the two-qubit interactions. The main technical ingredient of the algorithm is a generalized Kirkwood-Thomas ansatz for the ground state. The parameters of the ansatz are computed using perturbative expansions in powers of $\epsilon$. Our algorithm is closely related to the coupled cluster method used in quantum chemistry.