How many quantum gates do gauge theories require?

TL;DR

This paper analyzes the quantum gate complexity of simulating lattice gauge theories on digital quantum computers, highlighting the high costs and the importance of truncation schemes for practical implementation.

Contribution

It provides an assessment of gate requirements for lattice gauge theory simulations and emphasizes the impact of Hamiltonian truncations on computational feasibility.

Findings

Gate costs are high for current quantum hardware.

Truncation schemes significantly affect simulation complexity.

Low-dimensional truncations are crucial for practical quantum simulations.

Abstract

We discuss the implementation of lattice gauge theories on digital quantum computers, focusing primarily on the number of quantum gates required to simulate their time evolution. We find that to compile quantum circuits, using available state-of-the-art methods with our own augmentations, the cost of a single time step of an elementary plaquette is beyond what is reasonably practical in the current era of quantum hardware. However, we observe that such costs are highly sensitive to the truncation scheme used to derive different Hamiltonian formulations of non-Abelian gauge theories, emphasizing the need for low-dimensional truncations of such models in the same universality class as the desired theories.