发表机构
LTM Research, LTM; LTF Lab, L&T Finance（LTM 研究部，LTM; LTF 实验室，L&T 金融）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究将贷款组合优化建模为QCBO并转化为QUBO，采用泡利关联编码减少量子比特需求，在真实数据集上验证了变分量子算法在多达1500变量下可行，目标值与模拟差距小于10%。
AI 中文摘要
贷款组合优化（LPO）旨在寻找在满足实际选择约束的同时最小化信用风险的投资组合。考虑组合层面的风险不仅需要对预期损失进行建模，还需要对损失波动性和借款人违约相关性进行建模，这导致了一个大规模的组合优化问题，其复杂度随组合规模迅速增长。在本工作中，我们将LPO表述为一个二次约束二进制优化（QCBO）问题，该问题联合捕获预期损失和非预期损失，并将所得公式转化为适合变分量子优化的二次无约束二进制优化（QUBO）模型。为解决当前量子硬件量子比特资源有限的问题，我们采用泡利关联编码（PCE），该编码使得大量组合选择变量能够用相对较少的量子比特来表示。所提出的框架在一个包含2012名借款人的真实世界小额信贷数据集上进行了评估。对于包含多达1000个组合选择变量的问题实例，我们在匹配的时间预算下，将变分量子算法（VQA）的经典模拟与Google OR-Tools进行基准比较，在所有规模下均获得了目标值差距约为40%的可行组合。我们进一步在超导量子硬件上实现了该框架，用于包含多达1500个变量的实例。在这些实例中，实验获得的目标值在相应模拟结果的10%以内。这些发现证明了在当前量子硬件限制下，将基于PCE的变分量子优化应用于大规模贷款组合优化的可行性。
英文摘要
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.
Comments14 pages, 10 figures
