Quantum Genetic Optimization for Negative Selection Algorithms in Anomaly Detection

Anomaly detection is a foundational task in data science and cybersecurity, critical for identifying unusual patterns that may indicate fraud, intrusion, or system faults. Negative Selection Algorithms (NSA), inspired by the biological immune system's ability to distinguish self from non-self cells, have been widely applied for this purpose. Over the past decades, NSA variants such as the Real-valued Negative Selection Algorithm (RNSA) and its evolutionary extension EvoSeedRNSA have improved detection accuracy by employing genetic algorithms to optimize detector sets.

However, classical evolutionary algorithms face challenges in high-dimensional spaces due to the curse of dimensionality, leading to slow convergence and susceptibility to local optima. These limitations restrict NSA's scalability and effectiveness in complex real-world datasets. Concurrently, quantum computing has emerged as a promising paradigm, exploiting phenomena like superposition and entanglement to process information fundamentally differently from classical computers.

Quantum evolutionary algorithms, particularly Quantum Genetic Algorithms (QGA), combine evolutionary heuristics with quantum principles, enabling richer solution representations and potentially faster convergence. Despite growing interest, the integration of quantum algorithms with NSA remains underexplored, with few studies addressing practical implementations or empirical evaluations on real datasets. This gap motivates the present work to harness quantum advantages for enhancing NSA-based anomaly detection.

The core challenge addressed is the inefficiency and limited accuracy of detector generation in negative selection algorithms when applied to high-dimensional anomaly detection tasks. Specifically, classical genetic algorithms used in EvoSeedRNSA struggle with:

1. Large search spaces leading to slow convergence and computational overhead.

2. Loss of population diversity causing premature convergence to suboptimal detectors.

3. Difficulty balancing exploration of new solutions and exploitation of known good detectors.

These issues result in suboptimal anomaly detection performance, especially in complex datasets like financial transaction records with numerous features and subtle anomaly patterns. Improving detector generation efficiency and accuracy is essential to enable NSA methods to scale and perform robustly in practical anomaly detection scenarios.

This work introduces several key innovations:

1. Full integration of Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA framework, replacing classical genetic operators with quantum-inspired mechanisms.

2. Encoding detector features as qubit superpositions, allowing simultaneous representation of multiple candidate solutions and richer population diversity.

3. Application of quantum rotation gates to probabilistically adjust qubit amplitudes, dynamically guiding the population towards optimal solutions while preserving exploration.

4. Utilization of multiple quantum measurements (shots) per iteration to generate diverse detector candidates from a single quantum circuit.

5. Comprehensive empirical evaluation on a large-scale, real-world financial anomaly dataset, demonstrating practical performance gains and robustness.

These innovations collectively address classical NSA limitations by leveraging quantum computational principles, enabling more efficient and effective anomaly detector generation.

• �� Framework: The Quantum Genetic Negative Selection Algorithm (QGNSA) integrates Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA pipeline, replacing classical genetic optimization.

• �� Quantum Encoding: Each detector feature is represented by a group of qubits, with the number of qubits per feature determining encoding precision.

• �� Initialization: The quantum circuit is initialized with all qubits in equal superposition, representing a random population of candidate detectors.

• �� Measurement: Multiple shots of the quantum circuit produce a population of candidate detectors, exploiting quantum probabilistic outcomes for diversity.

• �� Fitness Evaluation: Each candidate detector's fitness is computed based on the proportion of anomalies detected, using Euclidean distance as the similarity metric.

• �� Quantum Rotation Update: Quantum rotation gates are applied to qubits to adjust probability amplitudes, steering the quantum state towards the best detected solution.

• �� Iteration: The process repeats for a predefined number of generations or until an optimal detector is found.

• �� Complexity: The algorithm's time complexity is O(MaxGen × PopulationSize × TrainSet), with optimizations focusing on fitness evaluation and quantum gate updates.

• �� Implementation: Classical components implemented in Python; quantum components simulated using Qiskit with matrix_product_state method for efficient quantum state management.

• �� Dataset: Metaverse Financial Transactions Dataset from Kaggle, containing 78,600 blockchain transaction records with 14 features.

• �� Preprocessing: Removed timestamp, IP prefix, addresses, risk score, and transaction type to avoid bias; normalized numerical features; one-hot encoded categorical features; split into self (72,105 samples) and anomaly (6,495 samples) sets.

• �� Validation: Employed 5-fold cross-validation on anomaly samples, with each fold used to generate detectors; repeated each fold 5 times for statistical robustness, totaling 25 runs per algorithm.

• �� Baselines: Compared QGNSA against classical EvoSeedRNSA.

• �� Metrics: Detection Rate (DR), False Positive Rate (FPR), and confusion matrix analyses.

• �� Quantum Simulation: Used Qiskit library with matrix_product_state to simulate quantum circuits and multiple measurements.

• �� Hyperparameters: Tuned population size, maximum generations, and qubit precision to balance accuracy and computational feasibility.

• �� QGNSA consistently outperformed classical EvoSeedRNSA, achieving over 5% higher detection rates and significantly lower false positive rates across all validation folds.

• �� Confusion matrices demonstrated improved true positive and true negative rates, confirming enhanced classification accuracy.

• �� The quantum encoding and rotation mechanisms maintained population diversity, preventing premature convergence observed in classical genetic algorithms.

• �� Although quantum simulation incurred higher computational cost, results indicate potential for acceleration on actual quantum hardware.

QGNSA is well-suited for anomaly detection in domains characterized by high-dimensional data and complex anomaly patterns, such as financial fraud detection, network intrusion detection, and industrial fault diagnosis. Its ability to efficiently generate diverse and accurate detectors makes it valuable for security monitoring systems requiring robust and timely anomaly identification. With future quantum hardware integration, QGNSA could enable real-time large-scale anomaly detection, transforming intelligent security and risk management practices.

• �� Validation limited to quantum simulators; real quantum hardware effects including noise and limited qubit counts remain untested.

• �� Feature encoding precision directly impacts quantum circuit size, posing scalability challenges.

• �� Experimental evaluation confined to a single financial dataset, limiting assessment of cross-domain generalization.