Anomaly Detection for Real-World Cyber-Physical Security using Quantum Hybrid Support Vector Machines

TL;DR

This paper explores the use of strong pre-processing methods and a quantum-hybrid Support Vector Machine (SVM) that takes advantage of fidelity in parameterized quantum circuits to efficiently and effectively flatten extremely high dimensional data.

Abstract

Cyber-physical control systems are critical infrastructures designed around highly responsive feedback loops that are measured and manipulated by hundreds of sensors and controllers. Anomalous data, such as from cyber-attacks, greatly risk the safety of the infrastructure and human operators. With recent advances in the quantum computing paradigm, the application of quantum in anomaly detection can greatly improve identification of cyber-attacks in physical sensor data. In this paper, we explore the use of strong pre-processing methods and a quantum-hybrid Support Vector Machine (SVM) that takes advantage of fidelity in parameterized quantum circuits to efficiently and effectively flatten extremely high dimensional data. Our results show an F-1 Score of 0.86 and accuracy of 87% on the HAI CPS dataset using an 8-qubit, 16-feature quantum kernel, performing equally to existing work and 14% better than its classical counterpart.

Figures (5)

• Figure 1: Hilbert-Schmidt inner product calculation for determining the fidelity of two feature-mapped values in the kernel, ($x_i$,$x_j$). A unitary $U(x_i)$ is performed, followed by its inverse $U^\dag(x_j)$. $S_{x_i}$ refers to the encoding circuit, while $G(x_i)$ refers to the unitary feature map operations. This calculation is repeated for all elements of $k(x_i,x_j)$ to establish the inner product matrix.
• Figure 2: HIL-based Augmented ICS (HAI) structure for steam-turbine and hydro-power. P1 (Boiler), P2 (Turbine), and P3 (Water Treatment) are all connected by P4, the overall controller that simulates a power grid model.
• Figure 3: Pipeline of the hybrid-quantum SVM anomaly detector. Pre-processing occurs classically, is turned into a fidelity inner-product kernel using a quantum computer, then utilized for SVM anomaly detection. Data kernels can then be passed into the trained SVM for detection of anomalies.
• Figure 4: The feature map. $N=n/2$ qubits are used to encode $n$ features. Data is encoded using generic rotation gates, or U gates, then entangled and rotated further. This circuit may be repeated multiple times (i.e., 3 times) to drive further interaction between qubits and features.
• Figure 5: Example of the 8-qubit fidelity kernel design on the HAI dataset for the train and test sets. Lower fidelity (green) means higher likelihood of the data being decided as anomalous. This can be seen in the test set kernel, where 1000 normal samples are provided followed by 500 anomalous samples.