Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model and high-temperature superconductor models

TL;DR

This paper presents resource-efficient algorithms for simulating the Fermi-Hubbard model and complex high-temperature superconductor models, enabling their study on early fault-tolerant quantum computers.

Contribution

It optimizes gate and qubit counts for these simulations and introduces algorithms for more realistic superconductor models with complex interactions.

Findings

Simulations of realistic superconductor models require only modestly more gates than Fermi-Hubbard.

Many instances are classically hard with fewer resources than typical quantum chemistry circuits.

Results suggest feasibility of studying high-temperature superconductors on early fault-tolerant quantum computers.

Abstract

Exploring low-cost applications is paramount to creating value in early fault-tolerant quantum computers. Here we optimize both gate and qubit counts of recent algorithms for simulating the Fermi-Hubbard model. We further devise and compile algorithms to simulate established models of cuprate and pnictide high-temperature superconductors, which include beyond-nearest-neighbor hopping terms and multi-orbital interactions that are absent in the Fermi-Hubbard model. We show that simulations of these more realistic models of high-temperature superconductors require only an order of magnitude or so more Toffoli gates than a simulation of the Fermi-Hubbard model. Furthermore, we find plenty classically difficult instances with Toffoli and qubit counts that far lower than commonly considered quantum phase estimation circuits for electronic structure problems in quantum chemistry. We believe our results pave the way towards studying high-temperature superconductors on early fault-tolerant quantum computers.