Landscape-Dependent Performance of Photonic Quantum Solvers in QUBO Feature Selection for Financial Risk Detection
Nirvik Sahoo, Paul Robert Griffin
Abstract
Feature selection for imbalanced classification tasks such as credit card fraud and consumer
default detection requires balancing predictive relevance, inter-feature redundancy, and com-
putational feasibility. We benchmark three computing paradigms, classical branch and bound
optimization (Gurobi), photonic entropic computing (QCI Dirac-3), and photonic boson sam-
pling (Piquasso∗), across thirteen feature-selection methods on two datasets: ULB Credit Card
Fraud (30 features) and AmEx consumer default (159 features). Each method class is routed
to the solver best matched to its mathematical structure and native capabilities: Gurobi solves
standard and graph-theoretic QUBOs to certified optimality with respect to the formulated
objective, Dirac-3 supports higher-order and integer-weighted objectives, and Piquasso samples
feature subsets via permanent-weighted sampling. On the ULB dataset, Dirac-3 MI-Spearman
using only 13 of 30 features reaches a mean F1 of 0.873 ±0.023 over five runs (best run 0.896),
and Piquasso is the best method at k=5. In contrast, the AmEx dataset shows no comparable
compression advantage, with performance improving steadily as more features are retained and
all three paradigms approaching F1 ≈0.80 only at large feature budgets (k=150). The AmEx
dataset also highlights a disconnect between optimization objective value and downstream pre-
dictive performance: for the distance-correlation method at k=25, Gurobi’s globally optimal
solution achieves F1 = 0.422, while Dirac-3 achieves a mean F1 of 0.746 on the same method.
Using Jaccard similarity to compare selected feature subsets, we find that solver and method
choices often produce different selections, but the performance impact of those differences is
strongly dataset-dependent: at matched feature budgets, F1 varies about ten times more across
methods on ULB than on AmEx. Overall, our results show that effective feature selection re-
quires balancing predictive relevance and redundancy against the computational capabilities of
the solver: specialized solvers matter most in compact, largely uncorrelated feature spaces, and
less in larger, more redundant ones.