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

2025-01-30

AI Summary

Classical simulation of the non-resonant, inhomogeneous open Tavis–Cummings model—including cavity dissipation and up to three excitations—suffers from exponential computational cost as the number of atoms (N) increases. Method: We propose two digital quantum simulation algorithms. First, we design a system-agnostic, fixed-interaction protocol that resolves the critical open-system challenge of sampling the Lindbladized fundamental matrix. Second, we construct quantum circuits for digital simulation of the Lindblad master equation, perform gate decomposition, and conduct error benchmarking under realistic noise models. Contribution/Results: The algorithms achieve gate complexities of (O(N^2)) and (O(N^3)), respectively, enabling polynomial scalability. Numerical validation confirms their capability to simulate large-(N) systems under noise, with accuracy verified against classical differential-equation solvers—demonstrating both fidelity and potential quantum advantage.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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 inhomogenous, 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 $O(N^3)$. 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)]. Furthermore, we benchmark our results against a classical differential equation solver and demonstrate the ability to simulate classically intractable systems.

Problem

• Quantum Systems
• Tavis-Cummings Model
• Non-resonant Interaction

Innovation

• Quantum Algorithms
• Tavis-Cummings Model
• Lindbladization Technique