Loan Portfolio Optimization with Variational Quantum Algorithms
Abstract
Loan portfolio optimization (LPO) seeks portfolios that minimize credit risk while satisfying practical selection constraints. Accounting for portfolio-level risk requires modeling not only expected losses but also loss variability and borrower-default correlations, leading to a large-scale combinatorial optimization problem whose complexity grows rapidly with portfolio size. In this work, we formulate LPO as a Quadratic Constrained Binary Optimization (QCBO) problem that jointly captures expected and unexpected losses and transform the resulting formulation into a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for variational quantum optimization. To address the limited qubit resources of current quantum hardware, we employ Pauli Correlation Encoding (PCE), which enables a large number of portfolio-selection variables to be represented using comparatively few qubits. The proposed framework is evaluated on a real-world microfinance dataset comprising 2012 borrowers. For problem instances with up to 1000 portfolio-selection variables, we benchmark classical simulations of a variational quantum algorithm (VQA) against Google OR-Tools under matched time budgets, obtaining feasible portfolios with an objective-value gap of about 40% across all sizes. We further implement the framework on superconducting quantum hardware for instances containing up to 1500 variables. Across these instances, the experimentally obtained objective values are within 10% of the corresponding simulation results. These findings demonstrate the feasibility of applying PCE-based variational quantum optimization to large-scale loan portfolio optimization under current quantum hardware limitations.
Related
- Qubit-Efficient Variational Quantum Optimization via Pauli Correlation Encoding: Application to Large-Scale Power Demand Portfolio Optimization
- Symmetry-guided algorithms for variational quantum optimization
- Resource Analysis of Quantum Optimization Algorithms via Variational Methods
- Optimization Geometry of QAOA and Variational Quantum Algorithms
- Accelerating noisy variational quantum algorithms with physics-informed denoising networks
BibTeX
@misc{bhargava2026loan,
title = {{Loan Portfolio Optimization with Variational Quantum Algorithms}},
author = {Balaganchi A. Bhargava and Kamlesh Kumar and Gouranga Dinda and Aniruddha Biswas and Vijay S. Rao and Debarag Banerjee and Arun Sehrawat},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30195},
eprint = {2609.30195},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30195},
}
RIS
TY - UNPB
TI - Loan Portfolio Optimization with Variational Quantum Algorithms
AU - Balaganchi A. Bhargava
AU - Kamlesh Kumar
AU - Gouranga Dinda
AU - Aniruddha Biswas
AU - Vijay S. Rao
AU - Debarag Banerjee
AU - Arun Sehrawat
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30195
UR - https://arxiv.org/abs/2609.30195
AB - Loan portfolio optimization (LPO) seeks portfolios that minimize credit risk while satisfying practical selection constraints. Accounting for portfolio-level risk requires modeling not only expected losses but also loss variability and borrower-default correlations, leading to a large-scale combinatorial optimization problem whose complexity grows rapidly with portfolio size. In this work, we formulate LPO as a Quadratic Constrained Binary Optimization (QCBO) problem that jointly captures expected and unexpected losses and transform the resulting formulation into a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for variational quantum optimization. To address the limited qubit resources of current quantum hardware, we employ Pauli Correlation Encoding (PCE), which enables a large number of portfolio-selection variables to be represented using comparatively few qubits. The proposed framework is evaluated on a real-world microfinance dataset comprising 2012 borrowers. For problem instances with up to 1000 portfolio-selection variables, we benchmark classical simulations of a variational quantum algorithm (VQA) against Google OR-Tools under matched time budgets, obtaining feasible portfolios with an objective-value gap of about 40% across all sizes. We further implement the framework on superconducting quantum hardware for instances containing up to 1500 variables. Across these instances, the experimentally obtained objective values are within 10% of the corresponding simulation results. These findings demonstrate the feasibility of applying PCE-based variational quantum optimization to large-scale loan portfolio optimization under current quantum hardware limitations.
ER -