Quantifying fault tolerant simulation of strongly correlated systems using the Fermi-Hubbard model

TL;DR

This paper assesses the potential of fault-tolerant quantum computers to simulate strongly correlated materials, specifically using the Fermi-Hubbard model, and highlights the current resource challenges involved.

Contribution

It provides an estimation of quantum resource requirements for simulating the Fermi-Hubbard model, revealing the need for advances in algorithms and hardware for practical applications.

Findings

Quantum resources needed are high for meaningful simulations.

Advances in quantum algorithms can reduce resource costs.

Hardware improvements are essential for feasibility.

Abstract

Understanding the physics of strongly correlated materials is one of the grand challenge problems for physics today. A large class of scientifically interesting materials, from high-$T_c$ superconductors to spin liquids, involve medium to strong correlations, and building a holistic understanding of these materials is critical. Doing so is hindered by the competition between the kinetic energy and Coulomb repulsion, which renders both analytic and numerical methods unsatisfactory for describing interacting materials. Fault-tolerant quantum computers have been proposed as a path forward to overcome these difficulties, but this potential capability has not yet been fully assessed. Here, using the multi-orbital Fermi-Hubbard model as a representative model and a source of scalable problem specifications, we estimate the resource costs needed to use fault-tolerant quantum computers for obtaining experimentally relevant quantities such as correlation function estimation. We find that advances in quantum algorithms and hardware will be needed in order to reduce quantum resources and feasibly address utility-scale problem instances.