arXiv 2501.185222025-01quant-phcs.DSphysics.comp-phphysics.optics

非共振开放Tavis-Cummings模型的数字量子模拟

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

备注：: 35 pages, 11 figures
发表信息：: Phys. Rev. Research 7, 043302 (2025)
DOI：: 10.1103/yflv-3s7t

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AI总结：

本文提出两种量子算法用于非共振开放Tavis-Cummings模型的模拟，解决了系统无关固定相互作用问题，展示了算法在不同场景下的有效性。

摘要：

开放的Tavis-Cummings模型由N个量子发射体与一个公共腔模相互作用，考虑了损耗和退相干，常用于量子信息处理和设计量子设备。随着N的增加，使用传统方法模拟开放的Tavis-Cummings模型变得越来越困难。为了解决这个问题，我们实现了两种量子算法，用于在非共振、非均匀的 regime 中模拟该模型的动力学，最多有三个腔内激发。我们证明所实现的算法的门复杂度以多项式方式增长，分别为O(N²)和O(N³)，而这些算法所使用的量子比特数量（空间复杂度）则以O(N)线性增长。其中一种算法是基于采样的波矩阵李普布拉德化算法，我们提出了两种协议来实现其系统无关的固定相互作用，解决了[Patel和Wilde, Open Sys. & Info. Dyn., 30:2350014 (2023)]中的关键开放问题。我们通过在各种场景下将结果与经典微分方程求解器进行基准测试，并展示了我们的算法能够准确重现预期的动力学。

英文摘要：

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.

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