Analogue quantum simulation with polylogarithmic interaction strengths by extrapolating within phases of matter

TL;DR

This paper demonstrates that for non-critical quantum systems, interaction strengths needed for simulation can be exponentially reduced by classical extrapolation, enabling more physically feasible quantum simulations.

Contribution

It introduces a method to simulate many-body quantum systems with polylogarithmic interaction strengths by extrapolating from smaller energy scales, avoiding large interaction requirements.

Findings

Interaction strengths scale polylogarithmically with inverse precision and system size.

Thermal states with exponential decay correlations can be simulated.

Ground states with a stable gap can be simulated using this method.

Abstract

Simple families of quantum Hamiltonians can simulate general many-body systems at arbitrary precision through the use of perturbative gadgets, however this generally requires interaction strengths spanning many orders of magnitude which scale polynomially in the system size and inverse precision, resulting in physically unrealisable systems. In this work, we show that for non-critical systems these required scalings can be exponentially reduced through classical post-processing, by simulating the model at smaller energy scales and extrapolating observables to the perturbative limit. In particular, we show that both local and extensive properties of thermal states with exponentially decaying correlations and ground states with a sufficiently stable gap can be simulated using gadgets whose interaction strengths scale only polylogarithmically in the inverse precision and the system size. As a key tool, we develop a generalised treatment of the local Schrieffer-Wolff transformation for geometrically quasi-local Hamiltonians over many energy scales, facilitating the analysis of perturbative gadget Hamiltonians without extensive global energy penalities, which may be of independent interest.