Benchmarking Quantum Neural Networks Developed for MBHB Coalescence in the Context of LISA Space Mission

Technical Summary: Benchmarking Quantum Neural Networks for MBHB Coalescence in the LISA Context

Problem Statement
The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GWs) from massive black hole binaries (MBHBs) weeks to months before coalescence. Achieving the scientific goals of low-latency alerts and multimessenger follow-up requires reliable, rapid detection and characterization of these signals within complex instrumental and astrophysical noise. While classical machine learning (ML) techniques, such as Support Vector Machines (SVMs) and deep learning architectures, have been applied to GW data analysis, the potential utility of Quantum Machine Learning (QML) for realistic astrophysical datasets remains an open question. This work addresses the need to systematically benchmark quantum, hybrid quantum-classical, and classical models against established baselines for two critical tasks: MBHB signal detection and merger time ($t_c$) estimation.

Methodology
The study utilizes the Sangria dataset from the LISA Data Challenge (LDC), which consists of a training dataset containing 15 consecutive MBHB GW signals embedded in realistic noise (including Galactic binaries and confusion foreground) and a blind dataset with undisclosed information.

1. Data Pre-processing:

   • Slicing: One-year time-series data were sliced into multiple samples using a moving window approach. For signal detection, 1,802 adjacent samples were generated; for merger prediction, 63,062 overlapping samples were created.
   • Labeling:
     • Signal Detection: Samples containing signals were labeled '1' (noisy GW), and isolated noise samples were labeled '0'.
     • Merger Prediction: Labels were assigned based on the time interval between the Innermost Stable Circular Orbit ($t_{ISCO}$) and the coalescence time ($t_c$), calculated using Newtonian approximations and frozen low-frequency assumptions.
   • Feature Extraction: Time-series data were mapped to compact feature vectors including power spectral density statistics (mean, standard deviation, max/min), spectral entropy, and peak frequencies.

2. Model Architectures:
   The authors implemented and compared a diverse set of models:

   • Quantum Models:
     • Variational Quantum Classifier (VQC): A parameterized quantum circuit with a feature map and trainable ansatz.
     • Post-VQC Hybrid Models: VQCs acting as feature extractors feeding into classical Neural Networks (NNs). Variants included:
       • Observables Construction Heuristic: Measuring observables of increasing locality.
       • Ansatz Expansion Heuristic: Evaluating circuits with shifted parameter configurations.
       • Combined Heuristic: Using both strategies.
     • Data Reuploading Classifier: A VQC architecture where input data is encoded multiple times throughout the circuit to enhance expressivity.
     • Quantum Kernel Methods: Using quantum feature maps to compute kernel matrices for classical SVMs.
     • Quantum Long Short-Term Memory (QLSTM): A hybrid model where LSTM gates are implemented via parameterized quantum circuits.
   • Classical Baselines: Standard implementations of SVMs, Multilayer Perceptrons (MLPs), Recurrent Neural Networks (RNNs), and LSTMs.

3. Evaluation:
   Models were trained on the labeled training dataset and evaluated on the blind dataset. Performance was measured via accuracy, F1 scores, recall (specifically for signal detection on blind data), and coalescence time localization errors (midpoint error and outside error).

Key Results

• GW Signal Detection:

  • Several quantum models achieved performance comparable to or exceeding classical baselines.
  • The Post-VQC model combining observables and ansatz expansion heuristics achieved perfect recall (1.00), correctly identifying all 1,802 signal samples in the blind dataset.
  • The standard VQC and Data Reuploading Classifier also performed strongly, with recalls of ~0.996, outperforming all classical NNs and the quantum kernel SVM.
  • Conversely, the QLSTM and Quantum Kernel SVM were outperformed by the classical SVM (recall 0.975), indicating that quantum advantage is not universal across architectures.
  • The Quantum Kernel SVM showed superior sample efficiency, reaching high accuracy with smaller training sets compared to the classical SVM.

• Merger Detection and Coalescence Time ($t_c$) Estimation:

  • Results diverged significantly from the detection task. The complex hybrid models that excelled at detection failed at localization.
  • The Post-VQC model combining both heuristics, despite perfect detection recall, failed to identify any merger events.
  • The standard VQC emerged as the most reliable model for this task. It successfully detected 5 out of 6 merger events and, crucially, produced predicted intervals that always contained the true coalescence time (zero outside error). It also achieved the smallest absolute midpoint errors (ranging from 249 s to 1410 s).
  • Classical models showed mixed results; the LSTM performed best among them, but the SVM exhibited catastrophic localization errors for specific signals.
  • Increased model complexity (e.g., deeper circuits, more parameters in Post-VQC variants) did not correlate with improved $t_c$ estimation and often degraded performance.

Key Contributions and Claims

1. Systematic Benchmarking: This work provides a comprehensive comparison of quantum, hybrid, and classical models on a realistic LISA dataset (Sangria), moving beyond theoretical proposals to empirical evaluation on blind data.
2. Task-Dependent Performance: The study demonstrates that the "best" quantum architecture is highly task-dependent. While hybrid Post-VQC models excel at binary signal detection, the simpler standard VQC is superior for precise coalescence time localization.
3. Complexity vs. Performance: The authors find that increasing architectural complexity (e.g., combining heuristics, increasing circuit depth) does not necessarily improve performance and can lead to overfitting or failure to generalize, particularly for regression-style tasks like time estimation.
4. Practical Utility vs. Quantum Advantage: The paper claims a practical benefit for specific QML configurations in GW analysis but explicitly does not claim a provable quantum advantage in the complexity-theoretic sense. The experiments were conducted on small-scale quantum simulations with feature-engineered inputs accessible to classical models.
5. Future Outlook: The results suggest that compact quantum models are promising candidates for future LISA data pipelines. As quantum hardware matures, these architectures could be scaled for end-to-end quantum processing and tested on larger datasets and noisy hardware.

Significance
The paper concludes that while no universal quantum advantage was observed, selected quantum models (specifically the standard VQC and specific hybrid configurations) offer competitive or superior performance for specific gravitational-wave analysis tasks compared to established classical methods. This validates QML as a viable component for future space-based GW data analysis, provided that model selection is tailored to the specific analysis goal (detection vs. parameter estimation) rather than assuming inherent superiority based on quantum nature alone.