Bayesian Quantum Orthogonal Neural Networks for Anomaly Detection

TL;DR

This work addresses anomaly detection in 3D objects from additive manufacturing by developing Bayesian (quantum) orthogonal neural networks (BONNs) that provide uncertainty-aware predictions. It introduces 3D orthogonal convolutions (OrthoConv3D) and Bayesian training over rotation angles in orthogonal quantum circuits, enabling efficient, stable learning with principled uncertainty quantification. The study demonstrates improvements in calibration (ECE) over point-estimate methods across classical and quantum-inspired architectures, and validates hardware feasibility through IBM Brisbane experiments, including fidelity assessments and robustness analyses. The results suggest that combining Bayesian inference with orthogonal, quantum-inspired layers enhances reliable anomaly detection in AM and points to scalable, hardware-amenable paths for quantum-assisted ML in real-world industrial contexts.

Abstract

Identification of defects or anomalies in 3D objects is a crucial task to ensure correct functionality. In this work, we combine Bayesian learning with recent developments in quantum and quantum-inspired machine learning, specifically orthogonal neural networks, to tackle this anomaly detection problem for an industrially relevant use case. Bayesian learning enables uncertainty quantification of predictions, while orthogonality in weight matrices enables smooth training. We develop orthogonal (quantum) versions of 3D convolutional neural networks and show that these models can successfully detect anomalies in 3D objects. To test the feasibility of incorporating quantum computers into a quantum-enhanced anomaly detection pipeline, we perform hardware experiments with our models on IBM's 127-qubit Brisbane device, testing the effect of noise and limited measurement shots.

Figures (9)

• Figure 1: Overview of the proposed anomaly detection pipeline using orthogonal neural networks. The 3D object (data point) is passed through 3D convolutional layers of the autoencoder, which are parametrised with orthogonal weight matrices. In the autoencoder framework, an Encoder compresses information to a 3D latent space, and a Decoder attempts to reconstruct the image from it. If the reconstruction is deemed successful, the object contains no anomaly. In the orthogonal 3D convolution, 3D patches (red) of a tensor object are flattened and treated as feature vectors. The 3D CNN kernels (grey) are flattened and form a matrix modelled by ortholinear quantum circuits (or quantum-inspired simulation) and multiplied with the flattened patches. The Loader circuit encoding this feature vector depicted is the 'diagonal' loader johri2021nearest. The orthogonal matrix multiplication corresponds to flattened 3D kernels. The orthogonal circuit shown is the 'pyramid' structure landman2022quantum. In the Bayesian framework, each orthogonal circuit parameter is sampled from a distribution, e.g. Gaussian with trainable mean and variance.
• Figure 2: (a) Parametrised quantum circuit for an $8 \times 8$ quantum orthogonal layer. Each vertical line corresponds to an $RBS$ gate with its angle parameter. And (b), a classical (non-orthogonal) neural network $8 \times 8$ layer. Courtesy landman2022quantum.
• Figure 3: Comparing uncertainty prediction approaches with feedforward architectures. Each plot shows a different metric, for each of the approaches. a) Expected Calibration Error (ECE), which is our quantifier of a robust predictor. b) The smallest detected anomaly (SDA) and largest undetected anomaly (LuDA) for each model. Finally, standard supervised metrics, d) Precision, e) Recall and f) F1-Score. For both FNN and QFNN architectures, we test point-estimate gradient descent (PE), Bayesian learning, Monte Carlo Dropout (MCD) and Ensembling. The latter are alternative uncertainty prediction methods. Focusing on the ECE as the primary metric (lower is better), we see the hybrid quantum FNN with Bayesian training outperforms all other models.
• Figure 4: Model uncertainty measured by ECE. Bayesian learning versus point-estimate gradient descent for classical and quantum (orthogonal) neural networks within autoencoder anomaly detection pipeline. Bayesian learning outperforms non-Bayesian methods relative to the Estimated Calibration Error (ECE), however orthogonality is less helpful for the more complex model architectures (3D-QCNN).
• Figure 5: A schematic diagram for showing convolution product reformulated as matrix multiplication for the 2D case (image courtesy kerenidis2019quantum). We model the $F^l$ matrix as an orthogonal matrix using quantum circuits.