Fault-tolerant quantum simulation of generalized Hubbard models

TL;DR

This paper introduces Tile Trotterization, a novel method for simulating complex Hubbard models on fault-tolerant quantum computers, improving efficiency and expanding applicability to materials and chemistry research.

Contribution

The paper presents Tile Trotterization, a new Trotter decomposition technique that generalizes plaquette Trotterization for arbitrary lattice Hubbard models and enhances simulation efficiency.

Findings

Tile Trotterization enables simulation of extended Hubbard models.

It scales more efficiently than qubitization for large systems.

The method broadens quantum simulation applications in materials science.

Abstract

Quantum simulations of strongly interacting fermionic systems, such as those described by the Hubbard model, are promising candidates for useful early fault-tolerant quantum computing applications. This paper presents Tile Trotterization, a generalization of plaquette Trotterization (PLAQ), which uses a set of tiles to construct Trotter decompositions of arbitrary lattice Hubbard models. The Tile Trotterization scheme also enables the simulation of more complex models, including the extended Hubbard model. We improve previous Hubbard model commutator bounds, further provide tight commutator bounds for periodic extended Hubbard models, and demonstrate the use of tensor network methods for this task. We consider applications of Tile Trotterization to simulate hexagonal lattice Hubbard models and compare the resource requirements of Tile Trotterization for performing quantum phase estimation to a qubitization-based approach, demonstrating that Tile Trotterization scales more efficiently with system size. These advancements significantly broaden the potential applications of early fault-tolerant quantum computers to models of practical interest in materials research and organic chemistry.