Polylogarithmic-Depth Quantum Algorithm for Simulating the Extended Hubbard Model on a Two-Dimensional Lattice Using the Fast Multipole Method

TL;DR

This paper introduces a quantum algorithm with polylogarithmic depth for simulating the extended Hubbard model on 2D lattices, utilizing the fast multipole method and recent neutral atom quantum computing advances.

Contribution

It presents a novel quantum simulation algorithm that efficiently handles long-range interactions in 2D lattice models using hierarchical approximations.

Findings

Circuit depth scales polylogarithmically with system size.

The method leverages recent neutral atom quantum computing techniques.

Efficient simulation of long-range interactions achieved.

Abstract

The extended Hubbard model on a two-dimensional lattice captures key physical phenomena, but is challenging to simulate due to the presence of long-range interactions. In this work, we present an efficient quantum algorithm for simulating the time evolution of this model. Our approach, inspired by the fast multipole method, approximates pairwise interactions by interactions between hierarchical levels of coarse-graining boxes. We discuss how to leverage recent advances in two-dimensional neutral atom quantum computing, supporting non-local operations such as long-range gates and shuttling. The resulting circuit depth for a single Trotter step scales polylogarithmically with system size.