Digital quantum simulations of the nonresonant open Tavis-Cummings model

The open Tavis-Cummings model consists of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi>N</b:mi> </b:math> 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, nonresonant regime, with up to three excitations in the cavity. We show that the implemented algorithms have gate complexities that scale polynomially, as <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>O</c:mi> <c:mo>(</c:mo> <c:msup> <c:mi>N</c:mi> <c:mn>2</c:mn> </c:msup> <c:mo>)</c:mo> </c:mrow> </c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>O</d:mi> <d:mo>(</d:mo> <d:msup> <d:mi>N</d:mi> <d:mn>3</d:mn> </d:msup> <d:mo>)</d:mo> </d:mrow> </d:math> , while the number of qubits used by these algorithms (space complexity) scales linearly as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>O</e:mi> <e:mo>(</e:mo> <e:mi>N</e:mi> <e:mo>)</e:mo> </e:mrow> </e:math> . 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 []. 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.