Lattice renormalization of quantum simulations

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 thorn 1D discrete nonAbelian D4 gauge theory with two spatial plaquettes.

Automated summary

This study introduces two schemes for determining Minkowski lattice spacings using tools from Euclidean lattice field theory, as well as advocates for a fixed-anisotropy approach to reduce circuit depth and number of independent simulations. These methods are demonstrated using qiskit noiseless simulators for a 2 thorn 1D discrete nonAbelian D4 gauge theory with two spatial plaquettes.