Digital Quantum Simulations of the Non-Resonant Open Tavis-Cummings Model

TL;DR

This paper develops and benchmarks two quantum algorithms for simulating the open Tavis-Cummings model with multiple emitters, achieving polynomial gate complexity and linear qubit scaling, suitable for quantum information processing.

Contribution

Introduces two scalable quantum algorithms for simulating the non-resonant open Tavis-Cummings model, including a novel implementation of the wave matrix Lindbladization protocol.

Findings

Algorithms scale polynomially with N in gate complexity.

Number of qubits scales linearly with N.

Algorithms accurately reproduce expected dynamics in benchmarks.

Abstract

The open Tavis--Cummings model consists of $N$ quantum emitters interacting with a common cavity mode, accounts for losses and decoherence, and is frequently explored for quantum information processing and designing quantum devices. As $N$ increases, it becomes harder to simulate the open Tavis--Cummings model using traditional methods. To address this problem, we implement two quantum algorithms for simulating the dynamics of this model in the inhomogeneous, non-resonant regime, with up to three excitations in the cavity. We show that the implemented algorithms have gate complexities that scale polynomially, as $O(N^2)$ and $O(N^3)$, while the number of qubits used by these algorithms (space complexity) scales linearly as $O(N)$. One of these algorithms is the sampling-based wave matrix Lindbladization algorithm, for which we propose two protocols to implement its system-independent fixed interaction, resolving key open questions of [Patel and Wilde, Open Sys. & Info. Dyn., 30:2350014 (2023)]. We benchmark our results against a classical differential equation solver in a variety of scenarios and demonstrate that our algorithms accurately reproduce the expected dynamics.