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Physica B Condensed Matter

Gauge transformation and A-B effect

Chun-Fang Li

Published Mar 1, 1997• 49 citations
Publisher
DOI
10.1016/s0921-4526(96)00530-3

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The Schrödinger equation of a charged particle in a uniform electric field can be specified in either a time-independent or a time-dependent gauge. The wave functions in these two gauges are related by a phase factor reflecting the gauge symmetry of the problem. We show that the effect of such a gauge transformation connecting the two wave functions can be mimicked by the effect of two successive extended Galilean transformations. An extended Galilean transformation connects two reference frames such that one is accelerating with respect to the other.
The simulation of quantum lattice gauge theories faces the major challenge of maintaining gauge invariance because various errors in the simulation push the state of the system out of the physical subspace of the system's exponentially larger Hilbert space. This paper outlines a method, based off of previous work [Phys. Rev. A 110, 022417 (2024)], that uses gauge transformations in two ways. First, the method exploits the Zeno effect by conducting frequent projections to suppress gauge drift. These projections utilize local gauge transformations to destructively interfere unphysical amplitudes via coupling to an ancillary qubit while the physical amplitudes are left untouched, up to a less than unity normalization factor. Second, gauge transformations are conducted throughout the time evolution of the system to hamper the speed of gauge drift. This paper demonstrates this method on a pure one-dimensional SU(2) toy model.
Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a nonperturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.