Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

TL;DR

This paper presents a variational quantum algorithm for black box binary optimization, demonstrated on feature selection tasks, showing competitive or superior results compared to classical methods in real-world applications.

Contribution

The paper introduces a novel variational quantum algorithm for unconstrained black box binary optimization and applies it to feature selection, with theoretical convergence guarantees.

Findings

Quantum algorithm achieves competitive performance on feature selection.

Demonstrates effectiveness using quantum hardware and simulations.

Outperforms some classical feature selection methods in certain metrics.

Abstract

We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution. To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection -- when formulated in terms of a generic loss function -- offers little structure on which to build classical heuristics, thus resulting primarily in 'greedy methods'. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry.