Digital Quantum Simulations of the Open Tavis-Cummings-Hubbard Model

The open Tavis-Cummings-Hubbard (TCH) model, which describes the behavior of a chain of coupled cavities which each contain multiple two-level systems, is useful for modeling optical and superconducting systems. These systems can be useful as simulators of condensed matter physics and lattice gauge theories. While cavity QED is difficult to simulate with classical computers, quantum algorithms can offer time and space complexity that is polynomial in system size, which is better than the best known classical methods. We implement one such algorithm which models loss by embedding Lindblad operators in a Hermitian matrix acting on a space including auxiliary qubits and Trotterizes both the unitary and lossy parts of the Lindbladian. We extend this algorithm, recently developed for single-cavity Tavis-Cummings systems, to simulate open Tavis-Cummings-Hubbard systems. We confirm the accuracy of our algorithm by benchmarking against classical simulations using the quantum trajectory method.