论文标题
用于财务指数跟踪的混合量子古典优化
Hybrid quantum-classical optimization for financial index tracking
论文作者
论文摘要
通过投资基准中包含的证券的加权子集，跟踪财务指数归结为复制其回报轨迹。即使对于由数十个或数百个资产组成的中等大型指数，选择最佳资产的最佳组合也成为一个具有挑战性的NP硬性问题，因此需要启发式方法来找到近似解决方案。与基于栅极的量子电路的杂化量子古典优化成为改善当前方案性能的合理方法。在这项工作中，我们引入了一种启发式修剪算法，以找到受基质性约束的资产的加权组合。我们进一步考虑了不同的策略来尊重这种约束，并通过数值模拟比较相关的量子Ansätze和经典优化器的性能。
Tracking a financial index boils down to replicating its trajectory of returns for a well-defined time span by investing in a weighted subset of the securities included in the benchmark. Picking the optimal combination of assets becomes a challenging NP-hard problem even for moderately large indices consisting of dozens or hundreds of assets, thereby requiring heuristic methods to find approximate solutions. Hybrid quantum-classical optimization with variational gate-based quantum circuits arises as a plausible method to improve performance of current schemes. In this work we introduce a heuristic pruning algorithm to find weighted combinations of assets subject to cardinality constraints. We further consider different strategies to respect such constraints and compare the performance of relevant quantum ansätze and classical optimizers through numerical simulations.
