quantlof 0.1.2

Quantum-enhanced Local Outlier Factor algorithm

QuantumLOFClassifier (Quantum Local Outlier Factor Classifier)

This package provides a quantum-enhanced version of the Local Outlier Factor (LOF) anomaly detection model, utilizing quantum computing tools such as Qiskit.

📘 Overview

QuantumLOFClassifier is an estimator based on the classical Local Outlier Factor (LOF) method, enhanced with quantum-based k-distance estimation using backends such as simulators or real quantum devices.

Note: Real quantum hardware execution is not yet tested.

• Quantum circuit execution via Qiskit AerSimulator or IBM Quantum Runtime
• Classical LOF concepts: k-distance, local reachability density (LRD), and LOF scores
• Anomaly detection based on a user-defined delta threshold
• Dual-model architecture: separate classifiers for clean and noisy data

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🔍 References

This implementation is inspired by the following paper:

• Ming-Chao Guo et al., Quantum Algorithm for Unsupervised Anomaly Detection
  • Section II.A: LOF definitions and thresholding (LOF(x) ≥ δ → anomaly)
  • Sections III.A–C: Quantum distance estimation, k-distance, LRD, and LOF calculations

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🚀 Example Usage

pip install quantlof

from quantum_lof import QuantumLOFClassifier

clf = QuantumLOFClassifier(
    n_neighbors=20,
    delta=1.5,
    quantum_backend='qiskit_simulator',  # or 'ibm_cairo', etc.
    shots=512,
    random_state=42
)

clf.fit(X_train, y_train)
anomalies = clf.get_anomaly_indices()
y_pred = clf.predict(X_test)
acc_clean, f1_clean, n_clean = clf.score_clean_only(X_test, y_test)

QuantumLOFClassifier – Compliance & Gap Report (vs. Guo 2023)

Last updated: 2025‑06‑04

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1  Executive summary (English)

The current QuantumLOFClassifier implementation partially follows the pipeline proposed in Guo et al., “Quantum Algorithm for Unsupervised Anomaly Detection” (arXiv 2304.08710, 2023).

• What is really quantum?  Only the pair‑wise distance estimation is executed on a quantum backend via a Hadamard‑test circuit.
• Where does it comply?  It respects Sec. III‑A Eq.(13–17) for turning an inner product into an Euclidean distance, and keeps the LOF formula (Sec. III‑B/C).
• Where does it diverge?  Every block that yields exponential‐speed‑up in the paper (QRAM, Quantum Minimum Search, Quantum Multiply‑Adder, amplitude estimation–based LOF, Grover‑style anomaly extraction) is replaced by classical code.

Overall, the code is a hybrid proof‑of‑concept rather than a strict end‑to‑end quantum algorithm.

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2  Quantum sub‑modules & level of compliance

Paper section	Purpose	Implemented?	Comment
III‑A Eq.(13–14)	Amplitude embedding of input vector	Partial	Uses StatePreparation; cost becomes exponential instead of ≈O(d).
III‑A Fig. 3	Hadamard test for ⟨x|y⟩	Yes	Circuit generated with ancilla‑controlled Uy†.
III‑A Eq.(15–17)	d(x,y)=√(2−2⟨x|y⟩)	Yes	Exact formula applied.
III‑A Step 1.6–1.7	Quantum Minimum Search (Grover)	No	Replaced by Python sort.
III‑B	Quantum multiply‑adder & average (LRD)	No	Classical loops.
III‑C Eq.(18)	Quantum LOF computation	No	Classical ratio/mean.
Eq.(2) & (28)	Grover anomaly extraction	No	Classical thresholding.

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3  Major divergences & limitations

1. Absence of QRAM  The paper assumes a QRAM oracle O_X; Qiskit/NISQ hardware do not provide this.
2. Quantum Minimum Search skipped  Sorting is done on CPU, losing the √m quantum speed‑up.
3. Quantum average / inverse missing  LRD & LOF are computed classically.
4. High circuit cost for StatePreparation  StatePreparation scales as O(2^n) gates, conflicting with the paper’s low‑depth assumption.
5. No amplitude‑estimation error control  Theoretical bounds (ε₁,ε₂,ε₃) are not implemented.
6. Fallback to classical path for n>100  The paper does not define such fallback; added for practicality.

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4  Practical recommendations

• Keep the current design for real datasets; full quantum blocks are unrealistic on today’s hardware.
• For small toy examples (<4 samples, <4 features) a pedagogical prototype of Quantum Minimum Search could be coded, but will not scale.
• Document clearly that the library is “quantum‑inspired” with a single quantum subroutine.

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