Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques

TL;DR

This paper introduces near-optimal quantum algorithms for simulating lattice gauge theories, achieving up to 25 orders of magnitude reduction in computational resources compared to traditional Trotter methods, especially for non-Abelian theories.

Contribution

It presents explicit circuit constructions and scalable algorithms that significantly reduce the complexity of simulating lattice gauge theories with fermions, surpassing prior Trotter-based approaches.

Findings

Up to 25 orders of magnitude reduction in simulation cost.

Polynomial scaling with the number of colors in gauge theories.

Efficient oracle-based algorithms exploiting operator sparsity.

Abstract

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find up to 25 orders of magnitude reduction in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first principles quantum simulation of chemistry.