Hybrid quantum–classical optimization with cardinality constraints and applications to finance
Samuel Fernández-Lorenzo, Diego Porras, Juan José García‐Ripoll · Quantum Science and Technology · 2021
Abstract In this work we develop tools to address combinatorial optimization problems with a cardinality constraint, in which only a subset of variables end up having nonzero values. Firstly, we introduce a new heuristic pruning method that iteratively discards variables through a hybrid quantum–classical optimization step. Secondly, we analyse the use of soft constraints in the form of ‘chemical potentials’ to control the number of non-zero variables. We illustrate the power of both techniques using the problem of index tracking, which aims to mimicking the performance of a financial index with a balanced subset of assets. We also compare the performance of different state-of-the-art quantum variational optimization algorithms in our pruning method.