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arXiv:2301.01836

A Quantum-Inspired Binary Optimization Algorithm for Representative Selection

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

Published Jan 4, 2023• 0 citations
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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.

DOI
10.48550/arxiv.2301.01836

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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.
Portfolio optimization, a core combinatorial optimization problem in quantitative finance, requires balancing return maximization and risk minimization within discrete asset sets. Classical algorithms often struggle with scalability and local optima traps when handling large-scale asset pools, limiting their practicality in dynamic markets. This study proposes a complete Quantum Approximate Optimization Algorithm (QAOA) workflow for portfolio optimization, from problem formalization to experimental validation. We first transform the portfolio optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) framework, then design a parameterized QAOA circuit with adjustable layers to balance expressiveness and noise resilience. We propose a methodology using Qiskit for quantum simulation and classical optimizers for parameter tuning, we propose implementing the algorithm on real-world S&P 500 stock data. We could also analyze the impact of quantum hardware noise and propose mitigation strategies, providing actionable insights for Noisy intermediate-scale quantum computing (NISQ)-era implementations. This work bridges quantum algorithm design with real-world financial applications, offering a theoretical framework for quantum-driven portfolio optimization.
Quantum finance represents a pivotal and cutting-edge application domain within the burgeoning field of quantum computing. In this work, we propose a two-step quantum approximate optimization algorithm (two-step QAOA) for portfolio optimization and risk assessment. The algorithm initiates by formulating the stock selection problem as a quadratic unconstrained binary optimization (QUBO) problem and employs a classical-quantum hybrid method to find the ground state of the Hamiltonian. We then introduce an energy-based characteristic indicator U∈[0,1), which quantitatively evaluates portfolio performance under customizable investment preferences, effectively capturing the trade-off between expected return and risk. The number of qubits required scales with the number of stocks N in the pool, and the number of Hamiltonian terms is O(N2). Numerical simulations show that the algorithm provides consistent and reasonable assessment results on both training and test datasets under different investment preferences (aggressive or conservative), validating the capability of the characteristic indicator to extract intrinsic information from the portfolios. Additionally, by incorporating warm-starting and digitized counterdiabatic techniques, the algorithm achieves improved scalability and faster convergence. Our work presents a flexible and practical algorithmic framework for applying quantum computing in the financial domain.
This study explores the integration of quantum computing techniques, specifically the Quantum Approximate Optimization Algorithm (QAOA), with classical portfolio optimization frameworks through the Quadratic Unconstrained Binary Optimization (QUBO) approach. Using monthly turnover data from the National Stock Exchange of India (NSE), this paper demonstrates the construction of a QUBO matrix by encoding expected returns and covariance-based risk profiles. Binary asset inclusion constraints are introduced into portfolios and then optimised using both brute force enumeration and quantum inspired solvers. The analysis reveals those combinations including Index Futures and Index Options exhibit superior risk-adjusted performance (Sharpe Ratio≈0.286\approx 0.286≈0.286). The hybrid approach suggests the promise of quantum inspired models as means to improve financial decision making under uncertainty. The results also give a robust template for scalable asset selection models that operate within the constraints of quantum computing infrastructure.
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.
Many applications in automated auditing and the analysis and consistency check of financial documents can be formulated in part as the subset sum problem: Given a set of numbers and a target sum, find the subset of numbers that sums up to the target. The problem is NP-hard and classical solving algorithms are therefore not practical to use in many real applications.We tackle the problem as a QUBO (quadratic unconstrained binary optimization) problem and show how gradient descent on Hopfield Networks reliably finds solutions for both artificial and real data. We outline how this algorithm can be applied by adiabatic quantum computers (quantum annealers) and specialized hardware (field programmable gate arrays) for digital annealing and run experiments on quantum annealing hardware.
Feature selection is crucial for enhancing the accuracy and efficiency of machine learning models. This work investigates the possibility of the usefulness of a quantum annealer to tackle the challenge of selecting features based on maximizing mutual information (MI) and conditional mutual information (CMI). Calculating the optimal feature set for maximum MI and CMI remains computationally intractable for large datasets on classical computers, even with approximation methods. This study employs a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) formulation, enabling its solution on a quantum annealer. Importantly, the study demonstrates the relevancy of this approach in identifying the best feature combinations that maximizes the MI and CMI. To showcase its real-world applicability, we apply MIQUBO to forecasting the price of used excavators. Our results demonstrate that using the MIQUBO approach there is an improvement in the prediction of machine learning models for datasets, with a smaller MI concentration on a subset of all features. • Problem Addressed: We tackle the computationally difficult problem of feature selection for machine learning models, specifically by maximizing mutual information (MI) and conditional mutual information (CMI) between features and the target variable. • Proposed Solution: We employ the adiabatic quantum computation paradigm to tackle this problem. The study utilizes a hybrid annealing approach, specifically the D-Wave Kerberos framework, which combines classical and quantum algorithms to solve the complex optimization problem. The feature selection task is reformulated as a Mutual Information Quadratic Unconstrained Binary Optimization (MIQUBO) problem, which can be solved on a quantum annealer. • Real-World Application: The MIQUBO method is applied to a practical, real-world scenario: forecasting the prices of used excavators. • Key Findings: The research demonstrates that using the MIQUBO approach leads to an improvement in the prediction performance of machine learning models. This is particularly true for datasets where the mutual information is less concentrated on a small subset of features.