Lattice Renormalization of Quantum Simulations

TL;DR

This paper introduces methods to relate trotterized quantum evolution operators to Euclidean lattice transfer matrices, enabling scale setting and continuum limit approaches in quantum simulations of field theories, demonstrated with a $D_4$ gauge model.

Contribution

It proposes two schemes for determining Minkowski lattice spacings from Euclidean data and advocates a fixed-anisotropy approach to improve quantum simulation efficiency.

Findings

Successfully applied methods to a 2+1D $D_4$ gauge theory using Qiskit simulators.

Demonstrated scale setting and continuum extrapolation techniques in quantum simulations.

Reduced circuit depth and simulation complexity through fixed-anisotropy approach.

Abstract

With advances in quantum computing, new opportunities arise to tackle challenging calculations in quantum field theory. We show that trotterized time-evolution operators can be related by analytic continuation to the Euclidean transfer matrix on an anisotropic lattice. In turn, trotterization entails renormalization of the temporal and spatial lattice spacings. Based on the tools of Euclidean lattice field theory, we propose two schemes to determine Minkowski lattice spacings, using Euclidean data and thereby overcoming the demands on quantum resources for scale setting. In addition, we advocate using a fixed-anisotropy approach to the continuum to reduce both circuit depth and number of independent simulations. We demonstrate these methods with Qiskit noiseless simulators for a $2+1$D discrete non-Abelian $D_4$ gauge theory with two spatial plaquettes.