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arXiv:2501.18522 · Physical Review Research

Digital quantum simulations of the nonresonant open Tavis-Cummings model

Aidan N. Sims, Dhrumil Patel, Aby Philip, Alex H. Rubin, Rahul Bandyopadhyay, Marina Radulaski, Mark M. Wilde

Published Sep 25, 2025• 1 citation
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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, nonresonant 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 []. 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.

DOI
10.1103/yflv-3s7t

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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, nonresonant 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 []. 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.
Tavis-Cummings (TC) cavity quantum electrodynamical effects, describing the interaction of NNN atoms with an optical resonator, are at the core of atomic, optical and solid state physics. The full numerical simulation of TC dynamics scales exponentially with the number of atoms. By restricting the open quantum system to a single excitation, typical of experimental realizations in quantum optics, we analytically solve the TC model with an arbitrary number of atoms with linear complexity. This solution allows us to devise the Quantum Mapping Algorithm of Resonator Interaction with NNN Atoms (Q-MARINA), an intuitive TC mapping to a quantum circuit with linear space and time scaling, whose N+1N+1N+1 qubits represent atoms and a lossy cavity, while the dynamics is encoded through 2N2N2N entangling gates. Finally, we benchmark the robustness of the algorithm on a quantum simulator and superconducting quantum processors against the quantum master equation solution on a classical computer.
Tavis-Cummings (TC) cavity quantum electrodynamical effects, describing the interaction of N atoms with an optical resonator, are at the core of atomic, optical and solid state physics. The full numerical simulation of TC dynamics scales exponentially with the number of atoms. By restricting the open quantum system to a single excitation, typical of experimental realizations in quantum optics, we analytically solve the TC model with an arbitrary number of atoms with linear complexity. This solution allows us to devise the Quantum Mapping Algorithm of Resonator Interaction with N Atoms (Q-MARINA), an intuitive TC mapping to a quantum circuit with linear space and time scaling, whose N+1 qubits represent atoms and a lossy cavity, while the dynamics is encoded through 2N entangling gates. Finally, we benchmark the robustness of the algorithm on a quantum simulator and superconducting quantum processors against the quantum master equation solution on a classical computer.
Abstract We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis–Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity–emitter systems on contemporary and future quantum computers.
We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open cavity quantum electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis-Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity-emitter systems on contemporary and future quantum computers.
We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open Cavity Quantum Electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis-Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity-emitter systems on contemporary and future quantum computers.
In this paper, we investigate the problem of simulating open system dynamics governed by the well-known Lindblad master equation. In our prequel paper [Patel and Wilde, Open Sys. & Info. Dyn., 30:2350010 (2023)], we introduced an input model in which Lindblad operators are encoded into pure quantum states, called program states, and we also introduced a method, called wave matrix Lindbladization, for simulating Lindbladian evolution by means of interacting the system of interest with these program states. Therein, we focused on a simple case in which the Lindbladian consists of only one Lindblad operator and a Hamiltonian. Here, we extend the method to simulating general Lindbladians and other cases in which a Lindblad operator is expressed as a linear combination or a polynomial of the operators encoded into the program states. We propose quantum algorithms for all these cases and also investigate their sample complexity, i.e., the number of program states needed to simulate a given Lindbladian evolution approximately. Finally, we demonstrate that our quantum algorithms provide an efficient route for simulating Lindbladian evolution relative to full tomography of encoded operators, by proving that the sample complexity for tomography is dependent on the dimension of the system, whereas the sample complexity of wave matrix Lindbladization is dimension independent.