Quantum fast-forwarding fermion-boson interactions via the polaron transform

TL;DR

This paper introduces a quantum algorithm that significantly reduces the computational complexity of simulating fermion-boson interactions, making it more feasible to study correlated quantum systems.

Contribution

The authors develop an efficient unitary transformation enabling fast-forwarded evolution, reducing complexity from polynomial to polylogarithmic in the bosonic cutoff parameter.

Findings

Complexity is polylogarithmic in the bosonic cutoff $\\Lambda$.

The method is applied to the Hubbard-Holstein model.

Potential for simulating fermion-boson interactions with resources similar to purely fermionic systems.

Abstract

Simulating interactions between fermions and bosons is central to understanding correlated phenomena, yet these systems are inherently difficult to treat classically. Previous quantum algorithms for fermion-boson models exhibit computation costs that scale polynomially with the bosonic truncation parameter, $\Lambda$. In this work we identify the efficient unitary transformation enabling fast-forwarded evolution of the fermion-boson interaction term, yielding an interaction-picture based simulation algorithm with complexity polylogarithmic in $\Lambda$. We apply this transformation to explicitly construct an efficient quantum algorithm for the Hubbard-Holstein model and discuss its generalisation to other fermion-boson interacting models. This approach yields an important asymptotic improvement in the dependence on the bosonic cutoff and establishes that, for certain models, fermion-boson interactions can be simulated with resources comparable to those required for purely fermionic systems.