Trotter化阈值与开放系统数字量子模拟中的耗散量子混沌
Trotterisation Thresholds and Dissipative Quantum Chaos in Open-System Digital Quantum Simulation
浏览论文内容
中文总结 AI 辅助
本研究证明开放系统数字量子模拟中Trotter化阈值依然存在，并基于随机矩阵理论提出统计方法表征耗散量子混沌，揭示耗散与酉混沌平衡时混沌涌现。
中文摘要 AI 辅助
数字量子模拟（DQS）是量子计算最有前景的应用之一。Trotter化的DQS通过将演化分解为一系列基于门的Trotter步骤来模拟量子动力学。使用更大的Trotter步骤可以减少所需的门数量，但目前已认识到，Trotter化步长不能超过某个阈值，超过该阈值后，由于量子混沌的出现，模拟精度会突然下降。迄今为止，这种行为仅针对不受环境噪声和退相干影响的封闭系统进行了研究，而现实世界的量子计算机对这些噪声和退相干高度敏感。在本工作中，我们研究了一系列实验相关的开放系统量子模拟器模型，并表明即使包含开放系统效应，Trotter化阈值仍然存在，甚至在长时间、稳态极限下，当所有相干性都已丧失时也是如此。我们表明，在阈值之前，开放DQS能够准确再现开放目标系统的动力学，但超过阈值后仍会出现突然的性能下降。我们引入了新的统计技术，基于随机矩阵理论（RMT），在封闭系统技术的基础上，严格表征Trotter化阈值之后量子混沌的出现，包括近似酉和真正的耗散量子混沌。最后，我们证明当耗散与潜在酉量子混沌的存在达到平衡时，耗散量子混沌会出现；耗散必须足够强以诱导真正的耗散行为，但又不能强到抑制潜在的混沌结构。
英文摘要
Digital quantum simulation (DQS) is one of the most promising applications of quantum computing. Trotterised DQS models quantum dynamics by decomposing the evolution into a sequence of gate-based Trotter steps. Using larger Trotter steps reduces the required gate count, but it is now understood that the Trotterisation step size cannot be increased beyond a certain threshold value, beyond which there is a sudden breakdown in simulation accuracy, due to the onset of quantum chaos. To date, this behaviour has only been studied for closed systems not subjected to the environmental noise and decoherence to which real-world quantum computers are highly sensitive. In this work, we study a range of experimentally relevant open-system quantum simulator models and show that Trotterisation thresholds persist even when open-system effects are included, even in the long-time, steady-state limit, once all coherence has been lost. We show that open DQS can accurately reproduce the dynamics of open target systems prior to the threshold, but still exhibits a sudden performance breakdown beyond it. We introduce new, statistical techniques to rigorously characterise the onset of quantum chaos beyond the Trotterisation threshold for both approximately unitary and genuine dissipative quantum chaos, based on random matrix theory (RMT), building on techniques developed for closed systems. Finally, we demonstrate that dissipative quantum chaos emerges when the dissipation is in balance with the presence of underlying unitary quantum chaos; the dissipation must be strong enough to induce genuinely dissipative behaviour, yet not so strong as to suppress the underlying chaotic structure.
发表机构
- University of Technology Sydney（悉尼科技大学）
- Sydney Quantum Academy（悉尼量子学院）
- University of Innsbruck（因斯布鲁克大学）
- PlanQC GmbH（PlanQC有限公司）
- Quantinuum
机构由 AI 辅助整理，请以论文原文为准。
