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

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

TL;DR

Open-Tavis–Cummings dynamics with losses pose classical simulation challenges, especially in non-resonant, inhomogeneous regimes. The authors implement two quantum-simulation approaches, Wave Matrix Lindbladization (WML) and Split J-Matrix, with explicit encodings for cavity and emitters and two fixed-interaction protocols, achieving polynomial gate complexities and linear qubit space. They validate accuracy against a classical solver across diverse scenarios, demonstrating access to parameter regimes inaccessible classically. The work broadens practical quantum simulation of open light-matter systems and provides concrete guidance for fixed-interaction implementation on near-term devices.

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.

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

TL;DR

Open-Tavis–Cummings dynamics with losses pose classical simulation challenges, especially in non-resonant, inhomogeneous regimes. The authors implement two quantum-simulation approaches, Wave Matrix Lindbladization (WML) and Split J-Matrix, with explicit encodings for cavity and emitters and two fixed-interaction protocols, achieving polynomial gate complexities and linear qubit space. They validate accuracy against a classical solver across diverse scenarios, demonstrating access to parameter regimes inaccessible classically. The work broadens practical quantum simulation of open light-matter systems and provides concrete guidance for fixed-interaction implementation on near-term devices.

Abstract

The open Tavis--Cummings model consists of 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 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 and , while the number of qubits used by these algorithms (space complexity) scales linearly as . 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.

Paper Structure

This paper contains 38 sections, 4 theorems, 151 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Paper Organization
  5. Notation
  6. Review
  7. Non-Resonant Open Tavis–Cummings Model
  8. Excitation-Number State to Qubit Mapping for Open TC Model
  9. Background on Trotterization
  10. J-Matrix and Split J-Matrix Algorithms
  11. Background on J-Matrix Algorithm
  12. Split J-Matrix
  13. Wave Matrix Lindbladization
  14. Background on Wave Matrix Lindbladization
  15. Realizing the Fixed Interaction exp(M Delta)
  16. ...and 23 more sections

Key Result

Theorem 1

Let $\mathcal{L}$ be a Lindbladian, as defined in eq:sum_coh_dis such that the Lindblad operators $L_{1}, L_{2}, \ldots, L_{K}$ commute with each other. The Split $J$-Matrix algorithm, represented as a quantum channel in eq:sJm-channel, uses the following number of one- and two-qubit gates such that where $\lambda_{\max}$ is defined in eq:split-lambda.

Figures (11)

  • Figure 1: Population of a resonant single-emitter system initialized with two excitations between $t = 0$ and $t = 0.25$ ns. The cavity is coupled to a single resonant emitter ($\omega_C = \omega_{E,1} = 245$ THz) and the system parameters are $(\kappa, \gamma, g_1) = (24.5, 0.4, 100)$ GHz. The top plot represents the result of the $J$-matrix quantum algorithm run on the QASM simulator, while the bottom plot represents the classical solution simulated in QuTiP. The simulation used 1000 shots, giving statistical shot noise of approximately $1/\sqrt{1000} \approx 0.03$.
  • Figure 2: Population of a driven resonant single-emitter system initialized with one photon between $t = 0$ and $t = 0.25$ ns. The cavity is coupled to a single resonant emitter ($\omega_C = \omega_{E,1} = 245$ THz) and the system parameters are $(\kappa, \gamma, g_1) = (24.5, 0.4, 100)$ GHz. The system also has a coherent drive of power $E_P=\kappa/2$. The top plot represents the result of the $J$-matrix quantum algorithm run on the QASM simulator, while the bottom plot represents the classical solution simulated in QuTiP. The simulation used 1000 shots, giving statistical shot noise of approximately $1/\sqrt{1000} \approx 0.03$.
  • Figure 3: Population of an off-resonant inhomogeneous $N=4$ emitter system initialized with one excitation between $t = 0$ and $t = 0.25$ ns. The cavity frequency is $\omega_C = 245$ THz and emitter frequencies are $(\omega_{E,i}) = (245.1, 245.2, 245.3, 245.4)$ THz. System parameters are $(\kappa, \gamma, g_i) = (24.5, 0.4, 100)$ GHz. The top plot represents the result of the Split $J$-matrix quantum algorithm run on the QASM simulator, while the bottom plot represents the classical solution simulated in QuTiP. The simulation used 1000 shots, giving statistical shot noise of approximately $1/\sqrt{1000} \approx 0.03$.
  • Figure 4: Population of an $N=9$ emitter system initialized with three excitations between $t = 0$ and $t = 0.25$ ns. The cavity frequency is $\omega_C = 245$ THz and the emitter frequencies are $\omega_{E,i}-\omega_C=\{100, -400, -100, 0, 100, 100, 400, -200, -500\}$ GHz. System parameters are $(\kappa, \gamma, g_i) = (24.5, 0.4, 100)$ GHz. The plot was generated by the Split $J$-Matrix algorithm run on the QASM simulator with 1000 shots, giving statistical shot noise of approximately $1/\sqrt{1000} \approx 0.03$.
  • Figure 5: Population of an $N=2$ emitter system between $t = 0$ and $t = 3$ ns. The cavity frequency is $\omega_C = 245$ GHz and the emitter frequencies are $\omega_{E,i} - \omega_C = (0.4, 1.3)$ GHz. System parameters are $(\kappa, \gamma, g) = (160, 19.6, 1000)$ MHz. The top plot was generated by a hybrid algorithm run on the QASM simulator and the bottom plot by QuTiP. The simulation used 1000 shots, giving statistical shot noise of approximately $1/\sqrt{1000} \approx 0.03$.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Theorem 1: Gate complexity of the Split $J$-Matrix algorithm
  • proof
  • Corollary 1
  • Theorem 2: Gate complexity of the LCU-based WML algorithm
  • proof
  • Corollary 2