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

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.

A novel feature selection method based on quantum support vector machine

“…Several studies have explored quantum feature selection approaches, including those based on a quadratic unconstrained binary optimization (QUBO) problem [7], Hamiltonian encoding and a ground state [8], quantum approximate optimization algorithm (QAOA) [5] and variational quantum optimization with black box binary optimization [6].…”

“…More recently, quantum computing has emerged as a promising platform for tackling computationally expensive combinatorial optimization tasks such as feature selection, offering innovative approaches to the challenges of dimensionality and data complexity [5][6][7][8]. This advancement complements the emergence of quantum machine learning, where quantum support vector machines (QSVM), demonstrate significant potential in leveraging quantum states for feature selection, transforming classical data into higher-dimensional Hilbert space for enhanced computational efficiency [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Variational Quantum Time Evolution without the Quantum Geometric Tensor

“…This makes it a promising candidate in settings where a good initial state can be constructed, e.g. in chemistry applications [9] or in classical optimization problems [10]. In quantum machine learning, the preparation of Gibbs states with imaginary-time evolution is a subroutine for quantum Boltzmann machines, which can, for example, be used in distribution learning or classification [11].…”