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Unsupervised quantum machine learning for fraud detection

Oleksandr Kyriienko, Einar B. Magnusson

arXiv:2208.01203v1quant-phcond-mat.dis-nn

TL;DR

Fraud detection must identify anomalous transactions among mostly genuine cases, including in a highly imbalanced credit-card dataset. The paper applies quantum kernels in one-class SVM anomaly detection and compares them with classical methods. Quantum kernels show a 15% average-precision increase over classical unsupervised learning, with the advantage growing at larger system sizes.

  • Problem

    Fraud detection seeks to identify anomalous transactions among a dominant number of nominal samples, and this paper targets credit-card fraud detection.

    Source: §I · p. 1

  • Method

    The authors use PCA-preprocessed credit-card data and quantum kernels in one-class SVM protocols, comparing results across feature and qubit counts with fine-tuned classical methods.

    Source: §I · p. 2, §V · p. 6

  • Results

    Quantum kernel methods show a 15% increase in average precision over classical unsupervised learning, with the advantage growing at larger system size.

    Source: §V · p. 7

  • Takeaways & Limitations

    The authors identify improved fraud-detection quality and possible detection of new fraud types as practical motivations for unsupervised approaches.

    Source: §IV · p. 5

    For datasets around 100,000 samples, full Gram-matrix calculation may take 16 weeks at MHz rates and 10^3 shots; partial randomized inference is proposed as a possible improvement.

    Source: §IV · p. 6

Abstract

from arXiv · show

We develop quantum protocols for anomaly detection and apply them to the task of credit card fraud detection (FD). First, we establish classical benchmarks based on supervised and unsupervised machine learning methods, where average precision is chosen as a robust metric for detecting anomalous data. We focus on kernel-based approaches for ease of direct comparison, basing our unsupervised modelling on one-class support vector machines (OC-SVM). Next, we employ quantum kernels of different type for performing anomaly detection, and observe that quantum FD can challenge equivalent classical protocols at increasing number of features (equal to the number of qubits for data embedding). Performing simulations with registers up to 20 qubits, we find that quantum kernels with re-uploading demonstrate better average precision, with the advantage increasing with system size. Specifically, at 20 qubits we reach the quantum-classical separation of average precision being equal to 15%. We discuss the prospects of fraud detection with near- and mid-term quantum hardware, and describe possible future improvements.

I. INTRODUCTION

Quantum machine learning has largely focused on supervised tasks, while several unsupervised areas remain under-explored. This work connects quantum kernels to unsupervised anomaly detection and tests fraud detection on credit-card transactions.

I. INTRODUCTION

  • Quantum computing has been explored for finance and data analysis, while near-term QML has emphasized feature-map encoding and supervised classification.Quantum linear-algebra subroutines are described as too costly for near-term operation.Source: §I · p. 1
  • Quantum clustering and related unsupervised methods remain under-explored compared with supervised QML, despite prior work on quantum PCA, kernel PCA, and q-means.The paper notes that these earlier methods target long-term fault-tolerant operation and primarily assume purely quantum data.Source: §I · p. 1
  • Fraud detection treats transactions as anomalies among mostly genuine samples, and the task is challenging when features are numerous and strongly correlated.Classical anomaly-detection approaches include distance- and density-based methods, Isolation Forest, deep anomaly detection, and kernel methods such as OC-SVM.Source: §I · pp. 1–2
  • The paper connects quantum kernels with unsupervised anomaly detection and evaluates one-class SVM fraud detection against optimized classical RBF-kernel results as feature and qubit counts increase.At 20 qubits, the reported quantum–classical separation reaches 15% in average precision.Source: §I · p. 2

II. FRAUD DETECTION: CLASSICAL BENCHMARKS

The section establishes supervised and unsupervised classical fraud-detection benchmarks using average precision and increasing feature counts. The RBF OC-SVM benchmark improves with more features before saturating near 0.55 average precision.

Classical benchmarks

  • The benchmark uses average precision rather than accuracy because the dataset is highly imbalanced and average precision evaluates precision across thresholds.The dataset has 492 fraud cases among 284,807 transactions and uses 28 anonymized features, excluding time and amount.Source: §II · p. 2
  • The manageable dataset is selectively sampled to include 500 transactions with 25 fraud examples, then standardized and reduced with PCA to vary feature count.The feature count corresponds to the number of qubits in the later quantum comparison.Source: §II · p. 2
  • Classical comparisons include supervised logistic regression and RBF-kernel SVC, plus unsupervised RBF-kernel OC-SVM; hyperparameters are selected by random search using cross-validation average precision.The authors note that using labels for validation in the unsupervised setting follows common research practice.Source: §II · pp. 2–3

Supervised detection (classification)

  • Tuned logistic regression improves gradually, while untuned performance peaks at five to ten features and deteriorates as feature count increases.The authors interpret the deterioration as overfitting at larger feature counts.Source: Figure 2 · p. 2, §II · p. 3
  • For SVC, the RBF kernel compares samples through a bandwidth-controlled function, and model construction requires pairwise kernel evaluations that scale as O(N_s^2).The section compares classical benchmarks with the later quantum-kernel approach.Source: §II · p. 3
  • For supervised SVC, average precision is slightly above logistic regression at five to ten features, then drops slightly at larger feature counts, likely from overfitting.These results set the supervised-classification benchmark, but supervised methods require prior fraud-case knowledge and do not generalize to new fraud types.Source: Figure 2 · p. 2, §II · p. 3

Unsupervised anomaly detection

  • The OC-SVM is built using confirmed nominal transactions, with transaction labels used to calculate average precision but not to train the model.Its ν parameter estimates the anomaly fraction.Source: §II · p. 3
  • Average precision for RBF OC-SVM rises with feature count, saturates near 0.55 at about 15 features, and changes little with tuning C and γ.The authors suggest that a slight decline at larger feature counts may reflect inability to use correlations from remaining principal components.Source: Figure 2 · p. 2, §II · p. 4

III. FRAUD DETECTION: QUANTUM APPROACH

The section develops quantum-kernel protocols for unsupervised anomaly detection and compares their performance with classical kernels. In simulations, re-uploaded IQP kernels achieve higher average precision at 20 qubits, while supervised quantum kernels also retain performance as feature counts grow.

III. FRAUD DETECTION: QUANTUM APPROACH

  • Quantum feature maps embed each input as an N-qubit state, whose overlap or local-Pauli measurements provide kernel values for the SVM Gram matrix.Overlap-based kernels can use return probabilities or SWAP and Hadamard tests; projected kernels compare local Pauli expectations.Source: §III · p. 4
  • At 20 qubits, the IQP kernel with d = 3 re-uploading reaches up to 15% higher AP than classical kernels.The reported result is for unsupervised fraud detection using OC-SVM.Source: Figure 4 · p. 4, §III · p. 5
  • Overlap-based and projected quantum kernels show similar performance under controlled kernel bandwidth, so the paper notes either can suit a particular system.Source: §III · p. 4
  • The study focuses on IQP circuits re-uploaded d = 3 times, with shallow random circuits between repetitions and no trainable quantum-circuit parameters.The repeated encoding is intended to increase circuit expressivity while avoiding coherent gate cancellation.Source: §III · pp. 4–5
  • In supervised classification, classical-kernel performance deteriorates beyond 10 features while quantum-kernel performance continues upward, reaching new highs around 17 features.The comparison is shown in Figure 4(a).Source: Figure 4 · p. 4, §III · p. 5
  • The authors identify potential for quantum kernels on correlated, multi-feature datasets that require unsupervised learning.Source: §III · p. 5

IV. DISCUSSION AND PERSPECTIVES

The discussion weighs the promise of quantum kernels for fraud detection against the resource demands of Gram-matrix training and inference. Its platform estimates suggest that large datasets may require partial or adaptive evaluation, and that near-term use may be better suited to prioritized checks than en-masse screening.

IV. DISCUSSION AND PERSPECTIVES

  • Quantum kernels can outperform classical kernels as feature-space size increases, supporting further consideration for unsupervised anomaly detection.Source: §IV · p. 5
  • Unsupervised detection may target potentially new fraud types, unlike simple classification; the authors estimate that a 15% detection-mechanism change could return £150 million to the UK economy.They cite a yearly billion pounds of fraud prevented in the UK as context for the estimate.Source: §IV · p. 5
  • Full Gram-matrix estimation scales as O(Ns^2), adding a sample costs O(Ns), and testing Nd incoming samples requires O(NdNs) kernel evaluations.The authors note that inference costs could hinder testing every incoming transaction.Source: §IV · pp. 5–6
  • For the 500-sample dataset, superconducting-circuit estimates range from 100 seconds to 28 hours for training, while trapped-ion estimates range from about 3 hours to 17 weeks.These estimates depend on processor rates and measurement-shot counts.Source: §IV · p. 6
  • For about 100,000 samples, full Gram training on MHz hardware with 10^3 shots may take 16 weeks, while randomized partial inference could reduce training to about 1 minute with O(Ns) scaling.The paper describes randomized protocols and adaptive detection as potential approaches.Source: §IV · p. 6
  • Photonic estimates give 17 minutes for 100,000-sample training at 10^3 shots, but deterministic optical gates are not yet established.Source: §IV · p. 6

V. CONCLUSIONS

The study develops kernel-based quantum protocols for unsupervised fraud detection and tests them against fine-tuned classical methods on a PCA-preprocessed credit-card dataset. In simulations up to 20 qubits, quantum kernels show a 15% increase in average precision over classical unsupervised learning, with the advantage growing at larger system sizes.

V. CONCLUSIONS

  • The protocols use quantum kernels with one-class support vector machines and were tested against fine-tuned classical methods on a PCA-preprocessed credit-card fraud dataset as feature count increased.Source: §V · p. 6
  • 15% increase in average precision over classical unsupervised learning was observed for quantum fraud detection, with the advantage growing at larger system sizes.Simulations ranged from a few to 20 qubits.Source: §V · p. 7
  • Further development calls for dataset-adapted kernel structures, while avoiding possible supervised-training data leakage that could bias unsupervised anomaly detection.Source: §V · p. 7
  • Training time, Gram-matrix construction, and measurement-shot requirements remain research challenges, especially for quantum hardware with lower operation rates.The authors suggest randomized or sparse Gram-matrix approaches and minimizing shots while keeping kernel measurements close to deterministic.Source: §V · p. 7
  • The timeline for quantum fraud detection depends substantially on whether the proposed approach can be simulated classically.Source: §V · p. 7

Disclaimer

The disclaimer states that the document is informational and is not investment research, investment advice, or a transaction recommendation. It disclaims representations, warranties, and liability concerning the document's information and potential effects.

Disclaimer

  • The document is for information purposes and is not investment research, investment advice, or a recommendation, offer, or solicitation concerning financial products or transactions.Source: Disclaimer · p. 7
  • HSBC Bank Plc. and its affiliates disclaim express or implied representations and warranties and accept no liability in connection with the paper.Source: Disclaimer · p. 7
  • The disclaimer specifically includes potential legal, compliance, tax, or accounting effects among the matters not covered by a representation or warranty.Source: Disclaimer · p. 7

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