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arXiv 2401.08142quant-ph
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论量子近似优化算法最优参数的实例依赖性：基于实例空间分析的见解

On the Instance Dependence of Optimal Parameters for the Quantum Approximate Optimisation Algorithm: Insights via Instance Space Analysis

Vivek Katial, Kate Smith-Miles, Charles Hill

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43 pages, 17 figures
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AI总结：

本文利用实例空间分析研究QAOA最优参数的实例依赖性，针对MaxCut问题提出基于实例特征的初始化方法QIBPI，提升了算法性能并验证了参数跨规模迁移的可行性。

摘要：

量子近似优化算法（QAOA）的性能依赖于电路每一层中最优参数的设置。这并非易事，且大量文献聚焦于在景观受到“贫瘠高原”等问题困扰时寻找最优参数的挑战。存在许多可用于搜索最优参数的优化启发式方法，每种方法都有各自影响性能的参数和初始化选择。最近，人们提出了这种最优参数搜索是否必要的问题，一些研究表明，对于特定类型的问题实例，最优参数往往集中在某些特定值上。然而，这些现有研究仅考察了 MaxCut 的特定实例类别，因此关于实例独立性的主张是否适用于多样化的实例范围尚不确定。在本文中，我们使用实例空间分析（Instance Space Analysis）来研究实例特征对 QAOA 性能的依赖关系。聚焦于 MaxCut 问题，我们评估了参数初始化策略的有效性，并引入了一种基于实例特征的全新初始化方法，称为量子基于实例的参数初始化（QIBPI）。本研究表明，在选择初始化参数时利用有关实例特征的见解可以提升 QAOA 的性能。我们还表明，在某些实例类别内，来自较小实例的参数可以迁移到较大实例中。本研究为量子算法的进一步实例空间分析奠定了基础，并鼓励考虑更广泛的实例类别，以确保结论不局限于特定的被充分研究的测试问题或类别。

英文摘要：

The performance of the Quantum Approximate Optimisation Algorithm (QAOA) relies on the setting of optimal parameters in each layer of the circuit. This is no trivial task, and much literature has focused on the challenge of finding optimal parameters when the landscape is plagued with problems such as "barren plateaus". There are many choices of optimisation heuristics that can be used to search for optimal parameters, each with its own parameters and initialisation choices that affect performance. More recently, the question of whether such optimal parameter search is even necessary has been posed, with some studies showing that optimal parameters tend to be concentrated on certain values for specific types of problem instances. However, these existing studies have only examined specific instance classes of MaxCut, so it is uncertain if the claims of instance independence apply to a diverse range of instances. In this paper, we use Instance Space Analysis to study the dependence of instance characteristics on the performance of QAOA. Focusing on the MaxCut problem, we assess the effectiveness of parameter initialisation strategies and introduce a new initialisation approach based on instance characteristics called Quantum Instance-Based Parameter Initialisation (QIBPI). This study reveals that using insights about instance characteristics in choosing initialisation parameters can improve QAOA performance. We also show that, within certain instance classes, parameters from smaller instances can be transferred to larger ones. This research provides a foundation for further instance space analysis for quantum algorithms and encourages a broader class of instances to be considered to ensure conclusions are not limited to particular well-studied test problems or classes.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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