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 ans\"{a}tze and classical optimizers through numerical simulations.

翻译：金融指数的跟踪归根结底是为了在明确的时间跨度上复制其回报轨迹,办法是投资于基准中包含的证券的加权子集。 选择资产的最佳组合成为一个具有挑战性的NP硬性问题,即使是由数十或数百项资产组成的中度大指数,也因此需要使用超速方法来寻找近似的解决办法。 混合量子经典优化和基于变式门的量子电路作为改善当前计划绩效的一种合理方法产生。 在这项工作中,我们引入了超速的裁剪算法,以找到受基本限制的资产的加权组合。 我们进一步考虑不同的战略来尊重这些限制,并通过数字模拟比较相关量子“{a}zze”和经典优化器的性能。