Towards Analog Quantum Simulations of Dynamical Gauge Theories

Abstract

A system which can implement an analog quantum simulation of lattice gauge theories has been proposed. In particular, the Schwinger model is formulated in terms of a lattice and superconducting qubit implementation is found which maps onto these dynamics. This thesis details the design of the superconducting circuit implementation of the model. The Hamiltonian of the superconducting circuit is designed to exhibit the gauge invariant dynamics of a U(1) symmetry. The gauge invariant set of states corresponds to those that are in the subspace of states that are shared by the Hamiltonian and the symmetry. Gauge invariance is simulated by looking at the dynamics of those states which obey a lattice version of Gauss' law. The device is simulated in an open quantum system and the measurable observables are extracted and mapped onto processes which can be observed in the lab. We nd that the dynamics occur over realistic time scales that can be observed with current laboratory equipment. These dynamics occur over hundred nanosecond timescales well within the minimum resolution of our equipment as well as well within the decoherence times of current superconducting devices.