Abstract
Abstract We study the quantum simulation of $Z_2$ lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e. with two temporal Wilson lines. Some results obtained by a simulator (with no hardware noise) and a real quantum computing device (with sizable hardware noise) are shown.
Highlights
Over the past few decades, lattice gauge theory has revealed many equilibrium properties of quantum field theory
The response of the system to the Wilson lines would be interesting. It is interpreted as gauge field dynamics induced by electric charges
Let us start with the basics of Z2 lattice gauge theory
Summary
Over the past few decades, lattice gauge theory has revealed many equilibrium properties of quantum field theory. One of the main issues is non-equilibrium or real-time dynamics of quantum field theory. Let us consider the Z2 lattice gauge theory without matter fields in 2+1 dimensions. In the classical simulations of pure lattice gauge theory, the most frequently-computed observable is the Wilson line or the Wilson loop. The Wilson line is interpreted as the world line of an electric charge At equilibrium, it is an order parameter for the phase of gauge theory. The response of the system to the Wilson lines would be interesting It is interpreted as gauge field dynamics induced by electric charges. We discuss how to perform the real-time simulation of pure lattice gauge theory with electric charges by quantum computers
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