Validating a Koopman-Quantum Hybrid Paradigm for Diagnostic Denoising of Fusion Devices

TL;DR

The paper tackles the input bottleneck of quantum machine learning for high-dimensional, chaotic classical data by introducing a physics-informed Koopman-Quantum hybrid framework. It builds a representation-level isomorphism between Koopman operator evolution and quantum dynamics, enabling a data distillation step that compresses waveforms into compact, quantum-ready features, followed by modular parallel quantum processing. Validated on 4,763 labeled channel sequences from 433 tokamak discharges, the method achieves 97.0% accuracy in screening corrupted diagnostics, matching state-of-the-art CNN performance with orders of magnitude fewer trainable parameters. The approach demonstrates a scalable, physics-grounded pathway for quantum-enhanced edge computing in constrained environments and lays groundwork for future multi-modal fusion diagnostics and cloud-based quantum deployment.

Abstract

The potential of Quantum Machine Learning (QML) in data-intensive science is strictly bottlenecked the difficulty of interfacing high-dimensional, chaotic classical data into resource-limited, noisy quantum processors. To bridge this gap, we introduce a physics-informed Koopman-Quantum hybrid framework, theoretically grounded in a representation-level structural isomorphism we establish between the Koopman operator, which linearizes nonlinear dynamics, and quantum evolution. Based on this theoretical foundation, we design a realizable NISQ-friendly pipeline: the Koopman operator functions as a physics-aware "data distiller," compressing waveforms into compact, "quantum-ready" features, which are subsequently processed by a modular, parallel quantum neural network. We validated this framework on 4,763 labeled channel sequences from 433 discharges of the tokamak system. The results demonstrate that our model achieves 97.0\% accuracy in screening corrupted diagnostic data, matching the performance of state-of-the-art deep classical CNNs while using orders-of-magnitude fewer trainable parameters. This work establishes a practical, physics-grounded paradigm for leveraging quantum processing in constrained environments, offering a scalable path for quantum-enhanced edge computing.

Figures (4)

• Figure 1: Overview of the diagnostic screening logic. The tokamak environment generates signal streams where valid physical data (Normal, blue) is frequently intermixed with stochastic corruptions (Anomaly, red). The objective is to map these high-dimensional inputs to a binary decision, distinguishing scientifically usable data from corrupted "Anomaly Warnings" to protect downstream analysis.
• Figure 2: Architecture of the Koopman-PQNN Framework. (a) Overview: The system ingests raw multi-channel diagnostics, processes them through the proposed hybrid architecture, and outputs a binary validity score. (b) Koopman Embedding Module: Raw chaotic signals are lifted into a linear space and reconstructed. (c) PQNN: To handle NISQ constraints, the feature vector is encoded and split across parallel Parameterized Quantum Circuits (PQCs), where each sub-circuit evolves features through variational layers.
• Figure 3: Comparison of training loss and test accuracy. The plots benchmark the proposed Koopman-PQNN (Red solid line) against four baselines: Raw-Data CNN (Grey dotted line), CNN on Koopman sequences (Blue dashed line), CNN on Koopman features (Green dash-dot line), and Classical multi-layer network (MLN) on Koopman features (Orange dash-dot line). (a) Training Loss: The curves demonstrate that all models successfully minimize the objective function and achieve stable convergence during the training process. (b) Test Accuracy: The evolution of testing accuracy indicates that while the computationally heavy Raw-Data CNN achieves a slightly superior performance ceiling ($\sim 98.0\%$), the proposed Koopman-PQNN and other physics-informed baselines all consistently converge to a comparable and robust accuracy level of $\sim 97.0\%$.
• Figure 4: Evolution of feature separability across different paradigms. The t-SNE projections visualize the test set samples (Orange: Stable, Blue: Anomaly) with their corresponding S-Score. (a) Raw Data (S=0.225) and (b) Koopman Sequences (S=0.458) illustrate the intrinsic difficulty of the task with heavy class overlap. (d) Raw-Data CNN (S=0.392) successfully separates classes but lacks cluster cohesion. (e) Koopman Seq CNN establishes the topological ceiling with the highest separation (S=0.810). (c) Our Method (Koopman-PQNN) achieves a remarkable S-Score of 0.800, significantly outperforming the classical (f) Feature CNN (S=0.754). This demonstrates that the lightweight quantum circuit matches the high-quality clustering of deep Koopman baselines while drastically outperforming the loose feature representation of the Raw-Data CNN.

Theorems & Definitions (14)

• Remark 1
• Definition 1: Koopman operator family
• Proposition 1: Basic properties of $U_K^t$
• Definition 2: Quantum evolution operator family
• Proposition 2: Basic properties of $\mathcal{U}^t$
• Theorem 3: Common time-translation structure
• Definition 3: Koopman eigenfunction
• Proposition 4: Multiplicative closure
• Definition 4: Hamiltonian eigenstate
• Remark 2: Formal spectral identification