Noise-Aware QNN Identifiability

Accuracy does not guarantee recoverability under noise.

Overview

This repository presents a controlled, fully reproducible micro‑study demonstrating a specific and important verification failure mode in noisy quantum (and quantum‑inspired) learning systems:

High predictive accuracy can coexist with a collapse of parameter identifiability.

In other words, a model may continue to perform well on its task while the underlying parameters become fundamentally non‑recoverable due to noise‑induced degeneracy in the loss landscape. When performance survives noise, identifiability may not.

This project is intentionally minimal. Its purpose is not to build a large framework, but to isolate and make visible a phenomenon that is often hidden by aggregate performance metrics.

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Problem / Phenomenon Investigated

In the presence of noise, many distinct parameter settings can become behaviorally indistinguishable: they produce nearly identical outputs on the task distribution.

In such regimes:

• Task accuracy may remain high.
• Loss values may appear well‑behaved.
• Gradient‑based optimization may still converge.

Yet recovering the generating parameters (or even determining whether recovery is possible) becomes ill‑posed.

In this repository, identifiability is defined operationally as follows:

Given data generated by a fixed ground‑truth parameter vector, can we reliably recover that vector (or detect that recovery is fundamentally unstable)?

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Hypothesis

As physically motivated noise increases:

• Task accuracy remains high, indicating behavioral success.
• Loss curvature collapses, producing flat or ill‑conditioned directions.
• Parameter recovery becomes unreliable, even when predictions remain correct.

This creates a verification gap between performance and recoverability.

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Method

Data Generation

• Binary classification labels are generated using a known, fixed ground‑truth parameter vector θ*.
• Inputs are randomly sampled and embedded via a simple normalized feature map.

Model

• A minimal QNN‑like forward function computes a score via the dot product between:
  • the embedded input vector, and
  • a normalized parameter vector.
• The sign of the score determines the predicted label.

This abstraction is deliberately lightweight to keep the phenomenon visible and interpretable.

Noise Model

Three lightweight, physically inspired noise proxies are applied to the embedded input:

1. Depolarizing‑like noise (p)
   With probability p, the embedded state is replaced by a random unit vector.

2. Phase‑like noise (σ)
   Additive Gaussian perturbation applied to the embedded state.

3. Correlated noise (γ) [NEW]
   Amplitude damping where all dimensions are affected by a common environmental factor. Models systematic errors like temperature fluctuations or power supply noise.

Noise is swept across multiple (p, σ, γ) regimes.

Purpose: Demonstrates that identifiability collapse is a general phenomenon, not specific to independent noise channels. See CORRELATED_NOISE.md for details.

Optimization

• A small random‑search optimizer is used.
• No deep learning frameworks are employed.
• This avoids optimizer‑specific artifacts and keeps dependencies minimal.

Metrics

Three core quantities are measured:

1. Task performance
   Classification accuracy.

2. Parameter recovery error
   ||θ̂ − θ*||₂.

3. Identifiability proxy
   A curvature‑based measure computed from a finite‑difference estimate of the Hessian diagonal:

   min |Hᵢᵢ| / max |Hᵢᵢ|.

   Values approaching zero indicate flat or ill‑conditioned loss directions, signaling poor identifiability.

Enhanced Identifiability Metrics

For rigorous analysis, the system supports Fisher Information Matrix analysis:

• Fisher Condition Number: κ(F) = λ_max / λ_min measures ill-conditioning
• Effective Rank: Participation ratio quantifies true dimensionality
• Effective Dimension: Number of well-determined parameter directions
• Fisher Trace: Total information mass

"Identifiability collapses because the information geometry becomes ill-conditioned."

See ENHANCED_METRICS.md for complete mathematical details.

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Results

Accuracy vs. Identifiability

Key result: high accuracy can coexist with identifiability collapse.

The identifiability axis is plotted on a logarithmic scale to emphasize near‑zero curvature collapse.

Parameter Recovery vs. Noise

Parameter recovery error generally increases with noise, but not necessarily monotonically due to finite‑sample effects and non‑convex optimization dynamics.

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Interpretation

This repository demonstrates a concrete evaluation failure mode:

Performance metrics alone are insufficient under noise.

Even when a model achieves strong predictive accuracy, the loss landscape may contain broad flat regions where many parameter settings are effectively equivalent. In such regimes:

• Parameter estimates become unstable.
• Interpretability degrades.
• Verification based solely on task performance becomes misleading.

This motivates the use of identifiability‑aware evaluation (and eventually identifiability‑aware objectives) in hardware‑relevant quantum machine learning systems and safety‑critical deployments.

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Reproducibility

Quick Start

From the repository root, run:

python -m src

This execution produces run artifacts in artifacts/latest/figs/:

• artifacts/latest/figs/fig_accuracy_vs_identifiability.png
• artifacts/latest/figs/fig_param_error_vs_noise.png

The curated, version-controlled figures used in this README are stored in assets/figures/.

Advanced Usage

The system provides comprehensive CLI and configuration capabilities:

# Custom noise sweep
python -m src --depolarizing 0.0 0.1 0.2 --phase 0.0 0.05 0.1

# Extended visualizations
python -m src --extended-viz --interactive

# Enhanced metrics with Fisher Information (rigorous identifiability analysis)
python -m src --enhanced-metrics

# Enhanced metrics with batch sampling (faster)
python -m src --enhanced-metrics --fisher-batch-size 50

# Configuration file
python -m src --config examples/single_experiment.yaml

# Batch experiments
python -m src --config examples/batch_experiments.yaml

Docs

• docs/QUICK_REFERENCE.md — fast start and common commands
• docs/PROJECT_SUMMARY.md — project scope and design intent
• docs/FEATURES.md — feature inventory and roadmap notes
• docs/CLI.md — full command-line interface
• docs/CONFIGURATION.md — YAML and JSON experiment configuration
• docs/ENHANCED_METRICS.md — Fisher Information and curvature metrics
• docs/ENHANCED_METRICS_INTEGRATION.md — integration notes and validation checks
• docs/VISUALIZATIONS.md — extended plotting and optional interactive output
• docs/DATA_EXPORT_LOGGING.md — results export, logging, and artifact layout
• docs/CORRELATED_NOISE.md — correlated noise model details

All results are deterministic under the fixed random seed specified in the code.

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Implementation Notes

• Language: Python
• Core dependencies:
  • numpy (numerical computation)
  • matplotlib (static plots)
  • scipy (Fisher Information, eigenvalue analysis)
• Optional dependencies:
  • plotly (interactive visualizations)
  • pyyaml (configuration files)
• No external quantum software development kits are required.
• The code is structured to emphasize clarity and reproducibility over performance.

Features

• ✅ Unit Tests: Comprehensive test coverage (56 tests)
• ✅ CLI Interface: Full command-line control
• ✅ Configuration System: YAML/JSON experiment definitions
• ✅ Extended Visualizations: Loss landscapes, trajectories, heatmaps
• ✅ Interactive Plots: Plotly-based dashboards
• ✅ Data Export: JSON/CSV/Pickle with metadata
• ✅ Logging: Structured experiment tracking
• ✅ Checkpointing: Resume long-running experiments
• ✅ Enhanced Metrics: Fisher Information Matrix analysis

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Tags

quantum machine learning ; quantum machine learning simulation ; neural quantum models ; variational quantum circuits ; verification ; identifiability ; noise robustness

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Why This Matters

For frontier research:
This work highlights a failure mode where models appear successful but are fundamentally non‑recoverable, relevant to interpretability, alignment, and verification research.

For space systems:
Verification under noise is critical for deployment in hardware‑constrained, safety‑critical environments where parameter instability can have downstream operational consequences.

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References

1. McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R., & Neven, H. (2018). Barren plateaus in quantum neural network training landscapes. arXiv:1803.11173.
2. Cerezo, M., Arrasmith, A., Babbush, R., et al. (2021). Variational Quantum Algorithms. arXiv:2012.09265. (Review of VQAs, including trainability and noise constraints.)
3. Wang, S., Fontana, E., Cerezo, M., et al. (2021). Noise-induced barren plateaus in variational quantum algorithms. Nature Communications 12, 6961. arXiv:2007.14384.
4. Stokes, J., Izaac, J., Killoran, N., & Carleo, G. (2020). Quantum Natural Gradient. Quantum 4, 269. arXiv:1909.02108.
5. Schuld, M., Bergholm, V., Gogolin, C., Izaac, J., & Killoran, N. (2019). Evaluating analytic gradients on quantum hardware. Physical Review A 99, 032331. arXiv:1811.11184.
6. Singkanipa, P., et al. (2025). Noise-induced barren plateaus and limit sets. Quantum (2025). (Extends the noise-induced landscape pathology story beyond the unital-noise setting.)

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Citations

If you use or build on this work, please cite:

Noise-Aware QNN Identifiability

@software{altman2025noise-aware-qnn-identifiability,
  author  = {Christopher Altman},
  title   = {Noise-Aware QNN Identifiability},
  year    = {2025},
  version = {0.1.0},
  url     = {https://github.com/christopher-altman/noise-aware-qnn-identifiability},
}

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License

MIT License. See LICENSE.

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Contact

• Website: christopheraltman.com
• Research portfolio: https://lab.christopheraltman.com/
• Portfolio mirror: https://christopher-altman.github.io/
• GitHub: github.com/christopher-altman
• Google Scholar: scholar.google.com/citations?user=tvwpCcgAAAAJ
• Email: x@christopheraltman.com

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Christopher Altman (2025)