Lattice Renormalization of Quantum Simulations

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 + 1D discrete non-Abelian D4 gauge theory with two spatial plaquettes.

Noise Improvements in Quantum Simulations of sQED using Qutrits

“…While [103] indicated it may not be necessary to use quantum simulations to set the scale, calculations of many different dynamical quantities will be effected by the noise of quantum computers and using a real-time correlator will provide a pessimistic estimate of the resources required to extract results from a quantum calculation.…”

“…The term, ĤBCH , is the Baker-Campbell-Hausdorff (BCH) Hamiltonian that is actually being simulated via Trotterization [103]. This Hamiltonian is…”

“…If we want to extract continuum physics, it is important to know what the lattice spacing is. Methods for this in regard to quantum simulations are currently being studied [103]. In order to determine the lattice spacing typically the mass of some particle of interest is used.…”

Gluon field digitization via group space decimation for quantum computers

“…This allows us to construct modified actions that can be studied nonperturbatively on classical computers today. For the eventual simulation on quantum computers, one can derive the modified Hamiltonian straightforwardly via the transfer matrix [50][51][52].…”

The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory

“…Here, we will investigate the discrete subgroup approximation [27][28][29][30] using classical lattice simulations. While performed in imaginary time, this nonperturbative study of truncation errors is known to be related to those in real time [31][32][33], thus providing us access to much larger systems than with current quantum devices. Discrete subgroups were studied in the early days of lattice field theory when memory limitations restricted the feasible lattice volumes due to the cost of storing SU (3) elements.…”