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.
Highlights
Inherent obstacles to classically simulating quantum field theories motivate developing quantum computer [1,2,3]
While large-scale, faulttolerant quantum computers will revolutionize our understanding of nature, for the foreseeable future, quantum computers will be limited to hundreds of nonerrorcorrected qubits with circuit depths less than 1000 gates–the so-called noisy intermediate-scale quantum (NISQ) era
To understand how renormalization arises in quantum simulations, it is useful to review the connection between the Kogut-Susskind Hamiltonian [96] and the Euclidean
Summary
Inherent obstacles to classically simulating quantum field theories motivate developing quantum computer [1,2,3]. Discretization reduces spacetime symmetries and introduce new operators into the LFT which are not present in the continuum theory that modifies the nonperturbative renormalization. In this paper we investigate the renormalization of LFT in Minkoswki spacetime due to trotterizing UðtÞ The consequence of this will be shown to be the introduction of a temporal lattice spacing, and new operators depending upon it which vanish in the Hamiltonian limit. We present a toy model, a D4 gauge group in 2 þ 1D with a two spatial plaquettes, to exemplify the power of a fixed anisotropy trajectory to extrapolate quantities to the continuum limit This requires as a first step to establish the scale setting for the lattice spacings, a; at, that can profit from our analytic continuation schemes.
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