A hybrid quantum-classical framework leveraging Grover's algorithm for financial anomaly detection with quadratic speedup over classical methods. Integrating quantum computing with classical preprocessing to identify statistical outliers across financial markets.
This research investigates a hybrid quantum-classical framework for detecting anomalies and outliers in financial markets. Traditional financial anomaly detection methods often suffer from high computational costs when scanning large datasets. By leveraging Grover's algorithm, which provides a quadratic speedup for unsorted search problems, this study integrates classical preprocessing with quantum data encoding to detect statistical outliers in key financial metrics.
Historical data from twenty technology stocks from the S&P500 were analyzed using three financial metrics: trailing P/E ratio, return on equity (ROE), and dividend yield. The hybrid approach combines classical z-score analysis with quantum search techniques to identify anomalies more efficiently than traditional methods.
Grover's algorithm provides O(√N) search complexity compared to O(N) classical methods, enabling faster anomaly detection in large datasets.
Combines classical preprocessing with quantum search, reducing computational overhead while maintaining accuracy and leveraging quantum advantages.
Analyzes multiple financial metrics simultaneously including P/E ratios, ROE, and dividend yields across 20 technology stocks.
Collected historical data from 20 top-performing technology stocks in the S&P500
(AAPL, MSFT, GOOG, AMZN, IBM, ORCL, INTC, NVDA, ADBE, CSCO, CRM, TXN, QCOM, HPQ,
DELL, ACN, AMD, AVGO, SAP, ADP) using the Python yfinance library.
Extracted three key financial metrics: trailing P/E ratio, return on equity (ROE),
and dividend yield.
Applied classical preprocessing by computing z-scores for each metric. Stocks exceeding a threshold of 2 standard deviations were flagged as outliers, generating binary indicators for quantum encoding.
Mapped binary indicators to computational basis states using five qubits (sufficient to represent up to 32 stocks). Constructed three separate quantum oracles using Qiskit's Diagonal gate, which applies phase flips (-1) to amplitudes of states corresponding to outliers.
Explored two encoding approaches:
Built Grover's algorithm circuits for each metric:
Simulated circuits using Qiskit's AerSimulator with realistic NISQ noise models derived from IBM quantum hardware. Noise models accounted for gate errors, readout errors, decoherence (T1 and T2 times), and crosstalk between qubits.
Post-simulation, measurement outcomes were analyzed to identify high-probability states corresponding to outlier stocks. Combined results from all three circuits into a composite anomaly score per stock.
The Grover circuits successfully identified outlier states with significantly higher probability amplitudes. Stocks like AMD, AVGO, and SAP showed anomalously high P/E ratios, while traditional dividend payers like HPQ were highlighted for dividend yield deviations.
While simulations ran on quantum simulators, the theoretical quadratic speedup of Grover's algorithm would provide significant advantages at larger scales. The algorithm completed searches with 1–2 iterations based on quantum counting estimates.
Experiments with realistic noise models revealed the trade-offs between circuit complexity and noise tolerance. While quantum counting accurately estimated thresholds, confidence decreased with noise, highlighting the importance of error mitigation techniques for practical applications.
The hybrid quantum-classical approach flagged the same set of outliers as pure classical z-score analysis, validating the correctness of the quantum implementation while demonstrating the potential for scalability advantages at larger data volumes.
This research demonstrates the feasibility of quantum-classical hybrid approaches for financial anomaly detection. Future improvements include: