A Quantum-Inspired Binary Optimization Algorithm for Representative Selection

TL;DR

This paper introduces a quantum-inspired binary optimization algorithm called the selector algorithm, designed for selecting representative data subsets that balance proximity and diversity, with applications in finance such as portfolio diversification.

Contribution

It formulates the representative selection problem as a QUBO, enabling quantum optimization methods to efficiently identify diverse and representative data subsets.

Findings

Successfully applied to synthetic datasets and real financial data

Demonstrated the algorithm's effectiveness in reconstructing the NASDAQ 100 index

Compared performance of two quantum annealers for portfolio diversification

Abstract

Advancements in quantum computing are fuelling emerging applications across disciplines, including finance, where quantum and quantum-inspired algorithms can now make market predictions, detect fraud, and optimize portfolios. Expanding this toolbox, we propose the selector algorithm: a method for selecting the most representative subset of data from a larger dataset. The selected subset includes data points that simultaneously meet the two requirements of being maximally close to neighboring data points and maximally far from more distant data points where the precise notion of distance is given by any kernel or generalized similarity function. The cost function encoding the above requirements naturally presents itself as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is well-suited for quantum optimization algorithms - including quantum annealing. While the selector algorithm has applications in multiple areas, it is particularly useful in finance, where it can be used to build a diversified portfolio from a more extensive selection of assets. After experimenting with synthetic datasets, we show two use cases for the selector algorithm with real data: (1) approximately reconstructing the NASDAQ 100 index using a subset of stocks, and (2) diversifying a portfolio of cryptocurrencies. In our analysis of use case (2), we compare the performance of two quantum annealers provided by D-Wave Systems.