Paper: arXiv 2301.01836

Authors: Anna G. Hughes, Jack S. Baker, Santosh Kumar Radha

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative quantum-inspired QUBO mapping for representative subset selection using custom similarity kernels. It provides solid practical application examples in index tracking and crypto diversification, though a deeper out-of-sample backtest would further solidify the empirical rigor.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Select most representative subset from large dataset using quantum optimization"] --> B["Problem Formulation:<br>Define QUBO Cost Function based on kernel similarity"]
    
    C["Data Inputs:<br>Synthetic Data, NASDAQ 100 Stocks, & Cryptocurrencies"] --> D["Computational Process:<br>Solve QUBO via D-Wave Quantum Annealers"]
    B --> D
    
    D --> E["Evaluation & Application:<br>(1) Index Tracking (NASDAQ 100)<br>(2) Portfolio Diversification (Crypto)"]
    
    E --> F["Key Findings:<br>Successfully constructs diversified portfolios & demonstrates practical financial utility of quantum annealing"]