Quantum Feature Engineering for Credit Default Prediction: When and Why IQP Circuits Help Linear Classifiers

Menachem Finkelstein; Diana Legziel Levy; Zohar Yakhini; Sarel Cohen

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Quantum Feature Engineering for Credit Default Prediction: When and Why IQP Circuits Help Linear Classifiers

Menachem Finkelstein, Diana Legziel Levy, Zohar Yakhini, Sarel Cohen

arXiv:2609.10505v1Sep 9, 2026cs.LGquant-ph

TL;DR

The paper asks whether IQP-derived features improve linear credit-default prediction over raw features and Kernel PCA at equal feature budgets. Using simulated IQP circuits and cross-validation, it finds a robust Logistic Regression gain, while benefits do not extend to other classifiers and depend on informative feature selection.

Problem
The paper tests whether IQP features improve credit-default prediction over raw features and Kernel PCA, where class imbalance, nonlinear interactions, and interpretability constrain the task.
Method
The study selects client attributes as rotation angles, extracts 2n expectation-value features from IQP circuits, and evaluates them with classifiers using cross-validation.
Results
IQP features improve Logistic Regression by +0.055 F1 over the raw baseline and +0.024 over Kernel PCA, while producing no benefit for Random Forest, SVM, XGBoost, or k-NN.
Takeaways & Limitations
The benefit is specific to linear models and depends on selecting informative inputs, with Random Forest-guided selection reaching F1 = 0.523 versus 0.496 for uncorrelated features.
Takeaways & Limitations
The circuits were evaluated on a classical simulator, so the study establishes predictive value rather than realized quantum speed-up; hardware noise and sampling costs remain unresolved.

Abstract

from arXiv · show

Credit default prediction is a tabular classification problem in which modest gains in F1 translate directly into reduced financial exposure. We ask whether Instantaneous Quantum Polynomial-time (IQP) circuits can produce features that improve a classifier over both its raw classical baseline and Kernel PCA - the strongest unsupervised classical non-linear alternative - at an equal feature budget. The dataset provides 23 financial attributes per client; for an n-qubit circuit we select n of them, encode each as a rotation angle, and read 2n expectation values back out as new features. The motivation for using a quantum circuit is computational: an n-qubit IQP circuit runs in constant depth and encodes feature correlations in a 2^n-dimensional Hilbert space, whereas classical simulation of its exact output statistics scales exponentially in n. Using the UCI Default of Credit Card Clients dataset and five-fold cross-validation, we find that appending 16 IQP features (n = 8 qubits) to a Logistic Regression model raises F1 from 0.462 to 0.517 (+0.055, p < 0.0001). Kernel PCA, the next-best method, reaches only 0.493 at the same feature count; the gap survives Benjamini-Hochberg correction across 12 tests (p = 0.00007). No other classifier - Random Forest, SVM, XGBoost, or k-NN - benefits, which points to a linear-expressivity mechanism rather than a generic improvement. We also show that how the 8 input features are chosen matters: Random Forest importance-guided selection reaches F1 = 0.523, while encoding maximally uncorrelated features drops it to 0.496, demonstrating that the circuit amplifies informative structure rather than creating it from scratch.

I. INTRODUCTION

The paper asks whether IQP-derived features can improve interpretable linear credit scoring over raw inputs and Kernel PCA at an equal feature budget. It frames quantum feature maps as embeddings whose measured observables encode nonlinear feature combinations.

I. INTRODUCTION: Credit default prediction combines class imbalance, nonlinear feature interactions, and regulatory pressure for interpretable models.The dataset contains 23 heterogeneous client attributes and approximately 22.6% defaults.
I. INTRODUCTION: Quantum feature maps embed classical inputs into a 2^n-dimensional Hilbert space, where observable expectation values become new features.The measured features can encode nonlinear combinations of the inputs.
I. INTRODUCTION: IQP features are evaluated against both the raw 23-feature Logistic Regression baseline and Kernel PCA, the strongest unsupervised nonlinear comparator.The comparison targets whether the quantum map captures structure missed by the best classical unsupervised alternative.
I. INTRODUCTION: The study contributes a nine-way equal-budget comparison, classifier-specific analysis, FDR-corrected testing, and feature-selection experiments.The feature-selection analysis reports that informative selection outperforms arbitrary choice, whereas uncorrelated inputs hurt performance.

B. IQP Circuits

IQP circuits use commuting diagonal operations interleaved with Hadamard layers and are motivated as constant-depth quantum feature maps. The paper positions them against interpretable Logistic Regression and stronger but less transparent classical models in credit scoring.

B. IQP Circuits: IQP circuits interleave Hadamard layers with diagonal commuting unitaries, offering depth independent of qubit count on quantum hardware.Their output distributions are believed hard to sample classically, while expectation values can be estimated by sampling.
B. IQP Circuits: Logistic Regression remains prominent in credit scoring because its coefficients are inspectable and individual decisions are auditable.Kernel SVMs and gradient boosting can be accurate but are harder to certify under model-risk frameworks.

A. Dataset

The method uses eight selected standardized features as angles in an 8-qubit IQP circuit, then appends 16 measured quantum features to the original 23 inputs. The circuit applies superposition, phase encoding, ring entanglement, and transverse measurement before classification.

A. Dataset: The 30,000-client UCI dataset contains 23 financial and demographic features plus six months of payment history, with a 22.6% default rate.Experiments use five-fold stratified cross-validation and report mean ± standard deviation over folds.
A. Dataset: Eight of the dataset’s 23 standardized features are clipped and converted to rotation angles using θ_i = x_i · π/3.The resulting eight angles are the circuit input.
B. IQP Quantum Feature Extraction: The circuit applies a Hadamard layer, RZ phase encoding, and ISINGZZ entanglement on an eight-qubit ring before measuring X and Y observables.The ring contains the wrap-around coupling between qubits 8 and 1; Z expectations vanish and are excluded.
B. IQP Quantum Feature Extraction: The 8-qubit circuit outputs 16 nonlinear X- and Y-basis features that are concatenated with the original 23 features into a 39-dimensional classifier input.The quantum circuit augments rather than replaces the classical representation.
B. IQP Quantum Feature Extraction: The IQP output features are nonlinear functions of all input angles and reflect inter-qubit entanglement rather than independent per-qubit contributions.Angle encoding is evaluated as a non-entangling control across the same five classifiers and feature budget.

C. Why This Circuit, and Why n = 8?

The design fixes n = 8 to emit 16 features, matching every classical comparator’s feature budget. The ring topology preserves constant-depth execution with linear gate count, while the circuit layers satisfy distinct encoding, interference, and connectivity requirements.

C. Why This Circuit, and Why n = 8?: n = 8 is fixed a priori because the circuit emits 2n = 16 features, exactly matching the classical comparison budget.Choosing n by performance would make feature budgets unequal and add an unaccounted degree of freedom.
C. Why This Circuit, and Why n = 8?: The ring topology uses n edges and two coupling sub-layers, preserving constant depth and O(n) gate count instead of all-to-all connectivity.For n = 8, the circuit has 24 gates at depth 4 before compilation.
C. Why This Circuit, and Why n = 8?: Phase encoding, the Hadamard layer, transverse read-out, and ring coupling respectively provide data loading, interference, measurable outputs, and scalable entanglement.The paper describes the encoding as a standard IQP feature map and makes no novelty claim for it.

D. Classical Comparison Methods

The comparison holds the augmented feature budget and training conditions constant while testing quantum features against classical transformations, nonlinear methods, and noise.

D. Classical Comparison Methods: The study also tests linear transformations, explicit degree-2 interactions, and random Gaussian features to distinguish useful nonlinearity from dimensionality inflation.PCA, SVD, ICA, random projection, and feature agglomeration form the linear control family.
D. Classical Comparison Methods: Kernel PCA provides the primary classical comparator because it is unsupervised, nonlinear, and produces abstract features without class-label access.Its RBF bandwidth uses the stated sklearn default.
D. Classical Comparison Methods: All augmented methods give Logistic Regression 16 additional features, producing 39 inputs and matching fitted parameter counts and training data across arms.Each transform is evaluated under the same fold partition, while only the content of the appended columns differs.

E. Classifiers

The evaluation spans five classifiers, combining a regularized, class-balanced Logistic Regression with four nonlinear alternatives.

E. Classifiers: Five classifiers are evaluated: Logistic Regression, Random Forest, SVM, XGBoost, and k-NN.The stated settings include balanced weighting for Logistic Regression and Random Forest, an RBF SVM, 100-tree XGBoost, and distance-weighted k-NN.

F. Statistical Testing

The study uses paired five-fold tests with Benjamini–Hochberg correction, and the reported pattern shows a significant Logistic Regression gain but no significant gains for nonlinear classifiers.

F. Statistical Testing: Paired t-tests across five cross-validation folds use α = 0.05, while Benjamini–Hochberg correction covers 12 planned comparisons.The correction controls the false-discovery rate across the stated test family.
F. Statistical Testing: Logistic Regression gains 0.055 F1 and 8.4 percentage points of accuracy, with both results at p < 0.0001.Table I reports means and standard deviations over five folds for models with and without 16 IQP features.
F. Statistical Testing: Random Forest, SVM, XGBoost, and k-NN remain statistically unchanged, with p > 0.05 on every reported metric.Several changes are smaller than one standard deviation, and the table caption identifies Logistic Regression as the only significant improver.
F. Statistical Testing: The classifier-specific pattern is consistent with quantum features supplying nonlinearity externally to a linear model rather than producing a generic benefit from extra inputs.Nonlinear classifiers already construct decision boundaries internally, so the appended features can be redundant for them.

B. Nine-Way Comparison at Equal Feature Budget

At an equal 39-feature budget, IQP features rank first for Logistic Regression and outperform KPCA after correction, while quantum-only features remain below the combined classical-quantum model.

B. Nine-Way Comparison at Equal Feature Budget: 0.055 F1 is the IQP gain for Logistic Regression, about 1.8× KPCA’s 0.031 gain; the quantum–KPCA gap has p = 0.00007.The comparison ranks nine feature-engineering methods at 39 features each, with quantum features first.
B. Nine-Way Comparison at Equal Feature Budget: Linear transformations change F1 by at most 0.001, polynomial degree-2 terms add 0.008, and random noise slightly reduces F1.These controls separate genuinely nonlinear feature maps from linear reparameterization and dimensionality inflation.
C. Multiple-Comparison Correction: IQP outperforms both the raw baseline and KPCA for Logistic Regression after Benjamini–Hochberg correction, while all eight nonlinear-classifier tests remain nonsignificant.Angle encoding beats the baseline but does not beat KPCA, leaving IQP as the only encoding with a corrected claim against the classical comparator.
B. Nine-Way Comparison at Equal Feature Budget: Quantum-only features reach accuracy 69.4% and F1 = 0.485, below 75.9% and F1 = 0.517 when combined with the original 23 features.Three parallel circuits encode all 23 input features while producing 46 quantum features.

E. Feature Selection Strategy Comparison

Feature selection materially changes IQP performance: informative, importance-guided inputs perform best, whereas uncorrelated inputs perform worst; covering all features costs more without surpassing the best targeted selection.

Feature-selection comparison: An 8-qubit circuit uses exactly 8 of the 23 available features, making feature choice a substantive design decision.Strategies S1–S4 append quantum features to the 23 classical features, while S5 uses three circuits and 69 total features.
Feature-selection comparison: F1 = 0.523 with RF importance-guided selection was highest, versus 0.517 for arbitrary first-8 and 0.516 for correlation-based selection.The RF procedure selects eight features ranked by mean decrease in Gini impurity, primarily payment-history and credit-limit variables.
Feature-selection comparison: F1 fell to 0.496 when the circuit encoded maximally uncorrelated features, significantly below first-8 selection at p < 0.01.The result supports selecting informative inputs rather than spreading encoding capacity across weakly predictive variables.
Feature-selection comparison: F1 = 0.519 from three circuits covering all 23 features remained below RF-guided selection while increasing the representation to 69 features.The broader coverage therefore offered no advantage over selecting the top eight features at lower feature cost.

A. How Large Is the Effect?

Appending 16 IQP features produces a substantial but incremental gain for Logistic Regression over its raw baseline and Kernel PCA at the same budget. The evidence supports a classifier-specific linear-expressivity mechanism rather than a universal improvement across models.

Effect size: Logistic Regression rose from F1 = 0.462 to 0.517, a +0.055 gain, while exceeding Kernel PCA by +0.024 at the same feature budget.Both comparisons survived Benjamini-Hochberg correction across 12 planned tests.
Effect size: The +0.055 F1 improvement also came with an 8.4-percentage-point accuracy increase and was about three fold-to-fold standard deviations of the augmented model.The augmented model’s fold standard deviation was ±0.017.
Effect size: The gain is real but incremental, and the paper does not claim that it justifies quantum hardware on its own.The reported transferable result is the mechanism: quantum features supply non-linear structure to a linear model beyond the strongest classical unsupervised alternative.
Effect size: Appending quantum features lifts Logistic Regression into a richer representation, whereas Random Forest, RBF-SVM, and XGBoost already implement non-linear transformations.This provides the proposed explanation for why the benefit is concentrated in the linear classifier.

D. Limitations

The reported IQP gains are confined to predictive value on a classical simulator, while hardware deployment remains constrained by sampling cost, noise, and unresolved robustness questions. Performance also depends on selecting informative input features rather than relying on the circuit to recover weak signals.

Hardware validity: Gate noise and decoherence could narrow the gap over Kernel PCA, so the advantage has not been established on near-term quantum devices.The paper identifies hardware evaluation with error mitigation as future work before drawing deployment conclusions.
Hardware cost: 6 × 10^8 circuit executions would be needed for the full 30,000-client design at two-decimal precision, making estimation error a practical hardware constraint.The required error would need to remain well below the +0.024 F1 margin and ±0.017 fold spread.
Scope of the claims: +0.055 F1 over the raw baseline and +0.024 over Kernel PCA were obtained for Logistic Regression, but these claims concern predictive value rather than realized quantum speed-up.The experiment used a classical simulator, and the n = 8-qubit statistics are described as trivially simulable.
Feature-selection boundary: F1 reaches 0.523 with Random Forest importance-guided inputs but falls to 0.496 for maximally uncorrelated features, limiting the method when encoded variables carry little outcome signal.The circuit amplifies interactions among informative inputs rather than creating predictive information from scratch.