Abstract
Over recent years, the relatively young field of quantum simulation of lattice gauge theories, aiming at implementing simulators of gauge theories with quantum platforms, has gone through a rapid development process. Nowadays, it is not only of interest to the quantum information and technology communities. It is also seen as a valid tool for tackling hard, non-perturbative gauge theory problems by particle and nuclear physicists. Along the theoretical progress, nowadays more and more experiments implementing such simulators are being reported, manifesting beautiful results, but mostly on dimensional physics. In this article, we review the essential ingredients and requirements of lattice gauge theories in more dimensions and discuss their meanings, the challenges they pose and how they could be dealt with, potentially aiming at the next steps of this field towards simulating challenging physical problems in analogue, or analogue-digital ways.This article is part of the theme issue ‘Quantum technologies in particle physics’.
Highlights
Gauge theories are fundamental in many modern physics contexts
In the case of fermionic matter, we can express the local charges as bilinears of the mode operators, e.g. Qa(x) = ψm† (x)(Ta)mnψn(x), where Ta are the suitable matrix representations of the generators, with [Ta, Tb] = ifabcTc
We have reviewed the challenges faced by the quantum simulation of lattice gauge theory (LGT) in more than one space dimension, from a theoretical point of view, which can be summarized in the following list of requirements: (i) Quantum simulators of LGTs with fermionic matter in more than 1 + 1d must allow for a way to describe the fermionic statistics
Summary
Gauge theories are fundamental in many modern physics contexts. Gauge invariance is the manifestation of a local symmetry, acting only on small local sets of degrees of freedom. We will provide a basic introduction to the theories in question, formulate a list of requirements which must be satisfied, bypassed or overcome in such simulators and discuss them: imposing gauge invariance on quantum simulators, dealing with fermionic matter, tailoring the complicated magnetic interactions and approximating infinite local Hilbert spaces by finite ones. The simulation can be analogue, involving a mapping of the Hamiltonian; stroboscopic or analoguedigital, in which different parts of the Hamiltonian are implemented sequentially, using shorttime pulses similar to quantum gates, based on the Trotter-Suzuki expansion [28] and possibly involving ancillary degrees of freedom; or completely digital, implementing the dynamics via a quantum circuit What all these approaches share is that one needs the simulator to encode the degrees of freedom, the Hilbert spaces, the symmetries and the interactions of the simulated model, whatever choice is made for the simulation approach. To discuss all that more concretely, let us zoom into the properties of the matter and gauge field Hilbert spaces
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