arXiv 2402.166922024-02quant-ph

噪声量子模拟：Tavis-Cummings模型和Heisenberg模型的性能与资源考虑

Noisy Quantum Simulation: Performance and Resource Considerations for the Tavis-Cummings and Heisenberg Models

Aalto University（阿尔托大学）

Alisa Haukisalmi, Daniel Paz Ramos, Matti Raasakka, Andrea Marchesin, Lauri Ylinen, Ilkka Tittonen

备注：: 47 + 13 pages, 28 figures, 3 tables; v2: Analysis and results have been significantly extended from the first version. We now explore both TCM and HSC systems with many different parametrizations. As a result, the conclusions drawn from the analysis are now more detailed and generally applicable
发表信息：: Phys. Rev. Research 7, 043254 (2025)

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AI总结：

本文研究了ZNE和ISL在Tavis-Cummings模型和Heisenberg自旋链中的性能，发现ISL在HSC中表现更优，但在TCM中因相互作用弱导致准确性下降，同时ISL在深层Trotter电路中更具鲁棒性。

摘要：

容错量子计算机有望模拟超越经典计算能力的复杂量子系统。相比之下，当前的噪声中等规模量子（NISQ）设备受限于硬件噪声。因此，量子模拟方法在短期内的应用仍然有限。两种主要技术用于解决这些挑战是零噪声外推（ZNE）和增量结构学习（ISL）。在本工作中，ZNE和ISL被用于模拟Tavis-Cummings模型（TCM）和Heisenberg自旋链（HSC）的 Trotter 化时间演化，使用经典模拟的噪声硬件后端。这些方法基于期望值的准确性与噪声less模拟相比，以及资源需求如电路深度和shot计数进行评估。此外，还研究了ISL中噪声对优化程序的影响，此前未被充分探讨。结果表明，ISL在HSC系统中表现更优，一致超越ZNE在期望值准确性方面。相反，在TCM中，尽管Trotter电路深度减少，ISL通常产生较低的准确性，弱相互作用常导致显著的相位滞后或平坦的期望值曲线。值得注意的是，当在无噪声条件下进行ISL优化时，该协议通常能够减少退相误差，但平均准确性仍因模拟的哈密顿量而异。我们的发现突显了量子模拟协议对哈密顿量编码系统动力学结构的敏感性。系统间的趋势表明，ISL优化受益于具有更强相互作用的Trotter电路，且ansatz构造更倾向于各向同性耦合。此外，尽管ISL引入了近似误差，但在具有更深Trotter电路的系统中，它比ZNE更具鲁棒性。

英文摘要：

Fault-tolerant quantum computers promise the simulation of complex quantum systems beyond the reach of classical computation. In contrast, current noisy intermediate-scale quantum (NISQ) devices are constrained by hardware noise. Consequently, quantum simulation methods remain limited in their near-term applicability. Two prominent techniques addressing these challenges are zero-noise extrapolation (ZNE) and incremental structural learning (ISL). In this work, ZNE and ISL are benchmarked for simulating the Trotterized time evolution of two models: the Tavis-Cummings model (TCM) and the Heisenberg spin chain (HSC), using a classically simulated noisy hardware backend. The methods are evaluated on the basis of the accuracy of expectation values relative to noiseless simulations and their resource demands such as circuit depths and shot counts. The impact of noise on optimization routines in ISL, previously underexplored, is also investigated. Results indicate that ISL performs more favorably in HSC systems, consistently surpassing ZNE in expectation value accuracy. Conversely, for the TCM, ISL generally yields lower accuracies despite reduced Trotter circuit depths, with weak interactions often leading to pronounced phase lags or flat expectation curves. Notably, when performing ISL optimization under noiseless conditions, the protocol is generally able to reduce dephasing errors, but average accuracies still vary on the simulated Hamiltonian. Our findings highlight the sensitivity of quantum simulation protocols to the structure of the Hamiltonian encoding system dynamics. Trends across systems suggest that ISL optimization benefits from Trotter circuits with stronger interactions, and that ansatz construction favors isotropic couplings. Moreover, although ISL introduces approximation errors, it demonstrates greater robustness than ZNE in systems with deeper Trotter circuits.

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