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arXiv 2408.14697quant-ph
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通过协同设计规避模拟量子机器学习算法中的陷阱

Circumventing Traps in Analog Quantum Machine Learning Algorithms Through Co-Design

Rodrigo Araiza Bravo, Jorge Garcia Ponce, Hong-ye Hu, Susanne F. Yelin

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10 pages, 6 figures
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AI总结：

本文研究模拟量子机器学习算法的景观陷阱问题，提出利用拟设的Magnus展开进行算法协同设计，以规避局部陷阱并确保在酉演化模拟中的良好收敛性与适用性。

摘要：

量子机器学习（QML）算法有望在含噪中等规模系统上实现近期可应用的量子计算。虽然大多数此类算法利用量子电路进行通用应用，但最近的一系列提案，即模拟量子机器学习（AQML）算法，打破了基于电路的抽象，转而倾向于利用量子系统的自然动力学进行计算，有望具备抗噪性并适用于量子模拟等特定应用。近期的AQML研究呼吁基于量子最优控制（QOC）理论确定最佳拟设选择实践，并探讨AQML算法是否具有无陷阱的景观。我们通过在两类模型上系统研究AQML景观来回应这一呼吁：一类是具有黑盒表达能力的模型，另一类是为模拟特定酉演化量身定制的模型。在数值上，第一类在其景观中表现出局部陷阱，而第二类是无陷阱的。然而，这两类模型都违反了QOC理论中保证无陷阱景观的关键假设。我们提出了一种方法，利用拟设的Magnus展开对用于酉演化模拟的AQML算法进行协同设计。我们展示了在模拟动力学方面的良好收敛性，并应用于计量学和量子化学。我们得出结论，这种协同设计对于确保AQML算法的适用性是必要的。

英文摘要：

Quantum machine learning QML algorithms promise to deliver near-term, applicable quantum computation on noisy, intermediate-scale systems. While most of these algorithms leverage quantum circuits for generic applications, a recent set of proposals, called analog quantum machine learning (AQML) algorithms, breaks away from circuit-based abstractions and favors leveraging the natural dynamics of quantum systems for computation, promising to be noise-resilient and suited for specific applications such as quantum simulation. Recent AQML studies have called for determining best ansatz selection practices and whether AQML algorithms have trap-free landscapes based on theory from quantum optimal control (QOC). We address this call by systematically studying AQML landscapes on two models: those admitting black-boxed expressivity and those tailored to simulating a specific unitary evolution. Numerically, the first kind exhibits local traps in their landscapes, while the second kind is trap-free. However, both kinds violate QOC theory's key assumptions for guaranteeing trap-free landscapes. We propose a methodology to co-design AQML algorithms for unitary evolution simulation using the ansatz's Magnus expansion. We show favorable convergence in simulating dynamics with applications to metrology and quantum chemistry. We conclude that such co-design is necessary to ensure the applicability of AQML algorithms.

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