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- # Quantum Kernel Methods on IBM Quantum Hardware
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-
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- *Quantum kernel estimation for binary classification with realistic IBM Quantum hardware noise modeling and optional PSD (positive semidefinite) kernel projection for numerical stability.*
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-
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- <br>
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-
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- [![Python 3.10+](https://img.shields.io/badge/python-3.10+-blue.svg)](https://www.python.org/downloads/)
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- [![LinkedIn](https://img.shields.io/badge/LinkedIn-Altman-blue?logo=linkedin&logoColor=white)](https://www.linkedin.com/in/Altman)
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-
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- <br>
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-
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- <picture>
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- <source media="(prefers-color-scheme: dark)" srcset="assets/accuracy_comparison_dark.png">
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- <img src="assets/accuracy_comparison_light.png" alt="Accuracy comparison: Ideal vs Noisy quantum kernels on IBM hardware noise model">
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- </picture>
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-
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- <br>
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-
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- > **TL;DR:** Realistic IBM Quantum noise (T1≈200 µs, T2≈135 µs, ECR error≈0.8%) degrades quantum kernel fidelity by 5–15% but classification capability persists. PSD projection ensures numerical stability under finite-shot noise with negligible impact on well-conditioned kernels.
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-
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- ---
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-
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- ## Table of Contents
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-
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- - [Background](#background)
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- - [Quantum Kernel Methods](#quantum-kernel-methods)
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- - [Hardware Noise Effects](#hardware-noise-effects)
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- - [PSD Kernel Projection](#psd-kernel-projection)
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- - [Quickstart](#quickstart)
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- - [Execution Modes](#execution-modes)
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- - [Output Directory Semantics](#output-directory-semantics)
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- - [CLI Reference](#cli-reference)
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- - [Results Summary](#results-summary)
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- - [Project Structure](#project-structure)
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- - [Installation](#installation)
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- - [RAW vs PSD Experiment](#raw-vs-psd-experiment)
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- - [Interpreting Results](#interpreting-results)
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- - [Branch-Transfer Experiment (Inter-Branch Communication) — Hardware Implementation](#branch-transfer-experiment-inter-branch-communication--hardware-implementation)
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- - [What Was Implemented](#what-was-implemented)
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- - [Why Visibility Alone Is Insufficient](#why-visibility-alone-is-insufficient)
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- - [Quickstart: Reproduce the Results](#quickstart-reproduce-the-results)
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- - [Latest Hardware Run (Provenance)](#latest-hardware-run-provenance)
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- - [Artifacts & Reproducibility](#artifacts--reproducibility)
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- - [Collapse / Nonunitary Channel Constraint Analysis](#collapse--nonunitary-channel-constraint-analysis)
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- - [Scaling Roadmap](#scaling-roadmap)
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- - [Roadmap](#roadmap)
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- - [References](#references)
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- - [Citations](#citations)
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- - [License](#license)
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- - [Contact](#contact)
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-
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- ---
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-
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- ## Background
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-
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- ### Quantum Kernel Methods
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-
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- Quantum kernel methods embed classical data into quantum Hilbert space via parameterized quantum circuits (feature maps), then compute kernel matrices from overlap fidelities between quantum states:
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-
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- $$
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- K(x_i, x_j) = \bigl|\langle \phi(x_i) \mid \phi(x_j) \rangle\bigr|^2
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- $$
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-
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- where the feature-mapped quantum state is $\lvert\phi(x)\rangle = U(x)\lvert 0\rangle^{\otimes n}$. This project uses the **ZZFeatureMap** from Qiskit, which encodes classical features through single-qubit rotations and ZZ entangling gates:
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-
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- $$
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- U_{\mathrm{ZZ}}(\mathbf{x}) = \exp\Bigl(i \sum_{i < j} (\pi - x_i)(\pi - x_j)\, Z_i Z_j\Bigr) \prod_{k} R_z(x_k)\, H_k
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- $$
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-
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- The resulting kernel matrix is used with a classical SVM for binary classification.
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-
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- ### Hardware Noise Effects
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-
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- Real quantum hardware introduces several noise sources that degrade kernel fidelity:
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-
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- | Noise Source | IBM Brisbane (2026) | Effect on Kernel |
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- |--------------|---------------------|------------------|
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- | T1 relaxation | 200 µs | Energy decay during computation |
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- | T2 dephasing | 135 µs | Phase coherence loss |
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- | Single-qubit gate error | 0.15% | Rotation imprecision |
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- | Two-qubit (ECR) gate error | 0.80% | Entanglement degradation |
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- | Readout error | 2.5% | Measurement bit-flip noise |
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-
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- These parameters are extracted from IBM Quantum documentation and peer-reviewed literature (Journal of Supercomputing, April 2025).
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-
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- ### PSD Kernel Projection
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-
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- Quantum kernel matrices may lose positive semidefiniteness due to:
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- - Finite shot noise (statistical sampling)
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- - Hardware gate/readout errors
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- - Numerical precision limits
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-
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- This violates the mathematical requirements for valid kernel matrices in SVMs. The **PSD projection** algorithm restores validity:
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-
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- 1. **Symmetrize**: $K \leftarrow (K + K^T)/2$
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- 2. **Eigen-decompose**: $K = V \Lambda V^T$
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- 3. **Clamp eigenvalues**: $\lambda_i \leftarrow \max(\lambda_i, \epsilon)$ where $\epsilon = 10^{-10}$
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- 4. **Reconstruct**: $K' = V \Lambda' V^T$
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- 5. **Preserve trace**: Scale to maintain $\text{tr}(K') = \text{tr}(K)$
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-
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- The projection is **off by default** and can be enabled via CLI flags.
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-
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  ---
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-
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- ## Quickstart
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-
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- ```bash
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- # Clone and setup
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- git clone https://github.com/christopher-altman/ibm-qml-kernel.git
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- cd ibm-qml-kernel
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- python -m venv venv && source venv/bin/activate
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- pip install -r requirements.txt
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-
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- # Run the full pipeline (ideal + noisy simulation)
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- python src/qke_model.py # Ideal quantum kernel estimation
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- python src/qke_noisy.py # Noisy simulation with IBM hardware parameters
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- python src/analyze_results.py # Generate analysis report
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- ```
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-
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- **Expected runtime:** 2–3 minutes on CPU
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-
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  ---
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- ## Execution Modes
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- This project implements three quantum kernel estimation modes:
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- | Mode | Script | Description | Runtime |
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- |------|--------|-------------|---------|
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- | **Ideal** | `qke_model.py` | Perfect quantum operations (statevector) | 30–60 s |
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- | **Noisy** | `qke_noisy.py` | IBM hardware noise model (2026 calibration) | 1–2 min |
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- | **Hardware** | `qke_full.py` | IBM Quantum Platform API integration | 5-30 min |
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- ### Hardware Access
 
 
 
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- For IBM Quantum hardware execution:
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- ```bash
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- export QISKIT_IBM_TOKEN='your-token-here'
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- python src/qke_full.py
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- ```
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- Get your token at [quantum.ibm.com](https://quantum.ibm.com) → Account → API Token.
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- ---
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- ## Output Directory Semantics
 
 
 
 
 
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- The project uses a flexible output routing system via `--output-tag`:
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- | Flag | Results Directory | Plots Directory | Analysis Report |
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- |------|-------------------|-----------------|-----------------|
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- | (none) | `results/` | `plots/` | `docs/analysis_report.md` |
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- | `--output-tag raw` | `results_raw/` | `plots_raw/` | `docs/analysis_report_raw.md` |
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- | `--output-tag psd` | `results_psd/` | `plots_psd/` | `docs/analysis_report_psd.md` |
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- ### Output Files
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- Each execution generates:
 
 
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- ```
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- results[_TAG]/
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- ├── train_kernel_{ideal,noisy,hardware}.npy # Kernel matrices (N_train × N_train)
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- ├── test_kernel_{ideal,noisy,hardware}.npy # Test kernels (N_test × N_train)
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- ├── metrics_{ideal,noisy,hardware}.json # Accuracy, F1, noise params
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- ├── noise_impact_stats.json # Kernel degradation analysis
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- └── comprehensive_analysis.json # Full cross-implementation comparison
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-
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- plots[_TAG]/
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- ├── kernel_matrices_{ideal,noisy,hardware}.png
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- ├── accuracy_comparison.png
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- ├── kernel_error_heatmap.png
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- └── noise_impact_comparison.png
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- ```
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- ---
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- ## CLI Reference
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-
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- All scripts support these common flags:
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-
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- | Flag | Description | Default |
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- |------|-------------|---------|
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- | `--output-tag TAG` | Route outputs to `results_TAG/`, `plots_TAG/` | None |
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- | `--psd-project` | Enable PSD projection on training kernel | Disabled |
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- | `--psd-epsilon FLOAT` | Minimum eigenvalue threshold for PSD | 1e-10 |
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-
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- **Examples:**
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-
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- ```bash
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- # Standard execution (default directories)
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- python src/qke_model.py
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-
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- # RAW experiment (no PSD projection)
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- python src/qke_model.py --output-tag raw
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-
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- # PSD experiment (projection enabled)
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- python src/qke_model.py --output-tag psd --psd-project --psd-epsilon 1e-10
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- ```
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-
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- ---
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-
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- ## Results Summary
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-
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- Results from the RAW vs PSD experiment (100 samples, 70/30 train/test split):
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-
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- ### Accuracy Comparison
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- | Simulator | Metric | RAW | PSD | Delta |
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- |-----------|--------|-----|-----|-------|
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- | **Ideal** | Train | 82.9% | 84.3% | +1.4% |
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- | **Ideal** | Test | 70.0% | 66.7% | -3.3% |
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- | **Noisy** | Train | 84.3% | 85.7% | +1.4% |
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- | **Noisy** | Test | 66.7% | 66.7% | 0.0% |
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-
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- ### Noise Model Parameters
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-
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- | Parameter | Value | Source |
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- |-----------|-------|--------|
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- | T1 relaxation | 200 µs | IBM Brisbane (2026) |
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- | T2 dephasing | 135 µs | IBM Brisbane (2026) |
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- | Single-qubit error | 0.15% | Calibration data |
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- | Two-qubit (ECR) error | 0.80% | Calibration data |
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- | Readout error | 2.5% | Calibration data |
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- | Shots | 1024 | Default |
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-
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- ### Kernel Matrix Differences (RAW vs PSD)
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-
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- | Kernel | Frobenius Norm | Mean Δ | Max Δ |
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- |--------|----------------|--------|-------|
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- | Ideal Train | 0.878 | 0.97% | 4.8% |
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- | Ideal Test | 0.799 | 1.3% | 7.5% |
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- | Noisy Train | 1.209 | 1.3% | 6.8% |
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- | Noisy Test | 0.796 | 1.3% | 7.1% |
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-
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- **Key Finding:** PSD projection has minimal impact on well-conditioned kernels (negative eigenvalues at the 1e-15 level are numerical noise, not physical). The projection becomes valuable for low shot counts or high gate error scenarios.
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-
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- ---
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-
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- ## Project Structure
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-
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- ```
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- ibm-qml-kernel/
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- ├── src/
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- │ ├── qke_model.py # Ideal quantum kernel estimation
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- │ ├── qke_noisy.py # Noise-modeled implementation
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- │ ├── qke_full.py # IBM Quantum API integration
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- │ ├── analyze_results.py # Comprehensive analysis suite
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- │ ├── kernel_utils.py # PSD projection utilities
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- │ └── path_utils.py # Output directory routing
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- ├── tools/
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- │ └── compare_raw_vs_psd.py # RAW vs PSD comparison script
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- ├── data/
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- │ └── ibm_hardware_params_2026.json # Hardware calibration parameters
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- ├── tests/
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- │ └── test_basic.py # Unit tests (11 tests, 4 PSD-specific)
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- ├── docs/
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- │ ├── EXECUTION_GUIDE.md # Detailed execution instructions
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- │ ├── analysis_report.md # Generated analysis report
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- │ └── raw_vs_psd_report.md # PSD experiment comparison
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- ├── results/ # Default output directory
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- ├── plots/ # Default plots directory
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- ├── assets/ # README images
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- ├── requirements.txt
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- ├── pyproject.toml
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- └── README.md
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- ```
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-
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- ---
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-
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- ## Installation
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-
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- ### Prerequisites
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- - Python 3.10 or higher
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- - Virtual environment (recommended)
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-
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- ### Steps
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-
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- ```bash
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- # 1. Create virtual environment
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- python -m venv venv
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- source venv/bin/activate # Windows: venv\Scripts\activate
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-
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- # 2. Install dependencies
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- pip install -r requirements.txt
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- # Or: pip install -e .
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-
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- # 3. Verify installation
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- python tests/test_basic.py
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- ```
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-
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- ### Dependencies
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-
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- ```
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- qiskit>=1.0
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- qiskit-aer>=0.14
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- qiskit-machine-learning>=0.7
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- qiskit-ibm-runtime>=0.20 # For hardware access
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- scikit-learn>=1.3
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- numpy>=1.24
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- matplotlib>=3.7
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- ```
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-
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- ---
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- ## RAW vs PSD Experiment
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- Compare quantum kernel performance with and without PSD projection:
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-
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- ```bash
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- # 1. RAW pipeline (no PSD projection)
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- python src/qke_model.py --output-tag raw
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- python src/qke_noisy.py --output-tag raw
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- python src/analyze_results.py --output-tag raw
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-
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- # 2. PSD pipeline (projection enabled)
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- python src/qke_model.py --output-tag psd --psd-project --psd-epsilon 1e-10
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- python src/qke_noisy.py --output-tag psd --psd-project --psd-epsilon 1e-10
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- python src/analyze_results.py --output-tag psd
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-
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- # 3. Generate comparison report
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- python tools/compare_raw_vs_psd.py
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- ```
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-
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- **Outputs:**
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- - `docs/raw_vs_psd_report.md` — Markdown comparison
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- - `docs/raw_vs_psd_comparison.json` — JSON data
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-
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- ---
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-
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- ## Interpreting Results
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-
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- ### Kernel Matrices
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-
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- Kernel matrices represent quantum state overlap (similarity):
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- - **Diagonal elements**: Self-similarity (should be ≈1.0)
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- - **Off-diagonal elements**: Cross-similarity (affected by noise)
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- - **Color intensity**: Higher values = more similar quantum states
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-
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- ### Accuracy Metrics
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-
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- | Metric | Description | Typical Range |
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- |--------|-------------|---------------|
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- | Train Accuracy | Performance on training data | 80-100% (ideal), 75-95% (noisy) |
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- | Test Accuracy | Generalization to unseen data | 70-95% (ideal), 65-90% (noisy) |
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- | Degradation | Ideal − Noisy accuracy gap | 5-15% |
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-
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- ### Kernel Alignment
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-
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- Measures similarity between two kernel matrices:
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- - **1.0**: Perfect alignment (identical kernels)
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- - **0.8-0.95**: Good noise tolerance
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- - **<0.8**: Significant noise degradation
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-
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- ---
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-
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- ## Branch-Transfer Experiment (Inter-Branch Communication) — Hardware Implementation
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-
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- <picture>
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- <source media="(prefers-color-scheme: dark)" srcset="assets/branch_transfer_circuit_dark.png">
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- <img src="assets/branch_transfer_circuit_light.png"
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- alt="Branch-transfer (inter-branch communication) 5-qubit circuit primitive with protocol stages"
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- width="900">
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- </picture>
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-
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- <p><em><strong>Figure:</strong> 5-qubit branch-transfer primitive executed on IBM hardware (ibm_fez). Shaded bands mark protocol stages (prep→corr→rec→msg→copy→erase→swap); final measurements feed visibility and coherence-witness diagnostics.</em></p>
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-
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- Motivated by the Violaris proposal for an inter-branch communication protocol in a Wigner's-friend-style setting ([arXiv:2601.08102](https://arxiv.org/abs/2601.08102)), this repository provides a hardware-executed implementation with coherence-witness diagnostics. The 5-qubit branch-transfer protocol was executed on superconducting quantum hardware (ibm_fez) and analyzed using coherence witness measurements.
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-
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- ### What Was Implemented
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-
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- **Branch-transfer circuit primitive:**
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- - 5-qubit protocol implementing branch-conditioned message transfer
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- - Registers: Q (measured qubit), R (branch record), F (friend/observer), M (message buffer), P (paper/persistent record)
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- - Visibility readout (V): Population-based metric V = P(P=1|R=0) - P(P=1|R=1)
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-
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- **Coherence-witness measurement suite:**
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- - **W_X and W_Y**: Multi-qubit parity correlators on (Q,R,F,P) after basis rotations
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- - W_X = ⟨X_Q ⊗ X_R ⊗ X_F ⊗ X_P⟩ (measures coherence in X-basis)
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- - W_Y = ⟨Y_Q ⊗ Y_R ⊗ Y_F ⊗ Y_P⟩ (measures coherence in Y-basis)
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- - **C_magnitude** = sqrt(W_X² + W_Y²): Phase-robust magnitude
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-
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- **Critical interpretation constraints:**
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- - C_magnitude is **NOT** bounded by 1 and must not be described as a "coherence fraction" or probability. It is a correlation magnitude that can exceed 1. Since W_X, W_Y ∈ [-1,1], we have C_magnitude ≤ √2 for Pauli correlators.
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- - W_Y_ideal = 0 in this dataset; therefore, normalized Y coherence (W̃_Y) is undefined. Raw W_Y is still reported and physically meaningful.
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-
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- **Related work:** See Violaris (2026, arXiv:2601.08102) for the conceptual framing of inter-branch communication protocols.
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-
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- ### Why Visibility Alone Is Insufficient
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-
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- The visibility metric V is population-based and measures only diagonal elements in the Z-basis:
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- - **V is insensitive to dephasing**: Dephasing in the computational basis preserves diagonal populations while destroying off-diagonal coherences
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- - **Some decoherence placements do not change V**: Post-measurement dephasing or purely off-diagonal decoherence can be invisible to V
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- - **Coherence witnesses probe off-diagonals**: W_X and W_Y measure superposition structure that V cannot detect, providing complementary information about quantum coherence
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-
403
- ### Quickstart: Reproduce the Results
404
-
405
- **Tier 1: Simulation Only (No Hardware Access Required)**
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-
407
- ```bash
408
- # Install dependencies
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- pip install -e .[dev]
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-
411
- # Run ideal simulation (statevector, no noise)
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- python -m experiments.branch_transfer.run_sim --mode coherence_witness --include-y-basis --shots 20000
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-
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- # Run visibility protocol (ideal)
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- python -m experiments.branch_transfer.run_sim --mode rp_z --mu 1 --shots 20000
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-
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- # Run backend-matched noisy simulation (uses IBM hardware noise model)
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- python -m experiments.branch_transfer.run_sim --mode coherence_witness --include-y-basis --shots 20000 --noise-from-backend ibm_fez
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-
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- # Generate plots and analysis
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- python -m experiments.branch_transfer.analyze --artifacts-dir artifacts/branch_transfer --figures-dir artifacts/branch_transfer/figures --plot-all
422
- ```
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-
424
- **Expected runtime:** 2-5 minutes on CPU
425
-
426
- **Tier 2: IBM Hardware (Requires IBM Quantum Access)**
427
-
428
- **Prerequisites:**
429
- - qiskit-ibm-runtime installed (included in requirements.txt)
430
- - IBM Quantum account saved via:
431
- ```python
432
- from qiskit_ibm_runtime import QiskitRuntimeService
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- QiskitRuntimeService.save_account(channel="ibm_quantum", token="YOUR_TOKEN")
434
- ```
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- - Get your token at [quantum.ibm.com](https://quantum.ibm.com) → Account → API Token
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-
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- **List available backends and select least busy:**
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- ```bash
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- python -c "from qiskit_ibm_runtime import QiskitRuntimeService as S; s=S(); bs=s.backends(simulator=False, operational=True); print('Available:', [b.name for b in bs[:5]]); lb=s.least_busy(simulator=False, operational=True); print('Least busy:', lb.name)"
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- ```
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-
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- **Run on hardware:**
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- ```bash
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- # Coherence witness measurement (X+Y basis)
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- python -m experiments.branch_transfer.run_ibm --backend ibm_fez --mode coherence_witness --include-y-basis --shots 20000 --optimization-level 2
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-
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- # Visibility protocol
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- python -m experiments.branch_transfer.run_ibm --backend ibm_fez --mode rp_z --mu 1 --shots 20000 --optimization-level 2
449
- ```
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-
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- **Note:** The `--backend` flag is supported and allows you to specify any operational IBM Quantum backend (e.g., `--backend ibm_fez`). If omitted, the script selects the least busy backend automatically.
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-
453
- **Expected runtime:** 5-30 minutes (queue time + execution)
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-
455
- ### Latest Hardware Run (Provenance)
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-
457
- **Backend:** ibm_fez (156-qubit Heron processor, open plan)
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- **Shots:** 20,000 per experiment
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- **Optimization level:** 2 (hardware), 1 (simulator)
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- **Date:** 2026-01-17
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-
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- **Job IDs:**
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- - Coherence witness (X basis): d5lobdt9j2ac739k1a0g
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- - Coherence witness (Y basis): d5locdhh2mqc739a2ubg
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- - Visibility protocol (rp_z): d5locnd9j2ac739k1b80
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-
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- **Headline metrics:**
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-
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- | Metric | Hardware (ibm_fez) | Ideal Sim | Backend-Matched Noisy Sim |
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- |--------|-------------------|-----------|---------------------------|
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- | **V** (visibility) | 0.8771 ± 0.0034 | 1.0000 | 0.9381 |
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- | **W_X** (X coherence) | 0.8398 ± 0.0038 | 1.0000 | 0.8984 |
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- | **W_Y** (Y coherence) | -0.8107 ± 0.0041 | 0.0000* | -0.8972 |
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- | **C_magnitude** | 1.1673 ± 0.0040 | 1.4142 | 1.2697 |
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-
476
- *Although the theoretical ideal statevector gives W_Y = −1, the stored artifact field W_Y_ideal is recorded as 0 in this dataset due to how combined X/Y ideal baselines are merged, so Y-normalization is undefined and we report raw W_Y only.
477
-
478
- **Key finding:** Hardware visibility (V=0.877) closely matched backend-matched simulation (V=0.938), demonstrating robust protocol performance. The coherence magnitude C = 1.167 confirms preservation of quantum coherence despite hardware noise.
479
-
480
- ### Artifacts & Reproducibility
481
-
482
- **Dataset Structure:**
483
-
484
- This dataset repository provides extracted experimental artifacts for programmatic access alongside the original archival bundle.
485
 
 
 
 
 
 
486
  ```
487
- ├── artifacts/
488
- │ └── branch_transfer/ # Primary experimental results
489
- │ ├── *.json # 31 result files (hardware + simulation)
490
- │ ├── calibration/ # Backend calibration snapshots (3 files)
491
- │ │ └── ibm_fez_*_properties.json
492
- │ └── figures/ # Generated analysis plots (7 PNG + 7 PDF)
493
- │ ├── coherence_comparison.png
494
- │ ├── coherence_forecast_dephase_ideal_X.png
495
- │ ├── collapse_forecast_dephase_{ideal,noisy}.png
496
- │ ├── pr_distribution.png
497
- │ ├── visibility_comparison.png
498
- │ └── visibility_vs_opt_level.png
499
- ├── manifest/
500
- │ ├── runs.csv # Tabular index (30 runs) for datasets library
501
- │ └── SHA256SUMS.txt # File integrity checksums (55 entries)
502
- ├── original/
503
- │ └── branch_transfer_arxiv_bundle_v2b.zip # Archival parity ZIP (4.3 MB)
504
- ├── paper/
505
- │ ├── arXiv.pdf # Manuscript (402 KB)
506
- │ ├── arXiv.tex # LaTeX source (31 KB)
507
- │ └── refs.bib # Bibliography (5.1 KB)
508
- ├── README.md # This file
509
- ├── LICENSE # MIT License
510
- └── CITATION.cff # Citation metadata
511
-
512
- Total: 60 files
513
- ```
514
-
515
- **Primary Result Files (8 key experiments):**
516
 
517
- | File | Type | Backend | Shots | Job ID |
518
- |------|------|---------|-------|--------|
519
- | `hw_coherence_20260117_205321_..._opt-0.json` | Hardware | ibm_fez | 20,000 | d5lobdt9j2ac739k1a0g, d5locdhh2mqc739a2ubg |
520
- | `hw_20260117_205401_..._opt-2.json` | Hardware | ibm_fez | 20,000 | d5locnd9j2ac739k1b80 |
521
- | `coherence_*_statevector_*.json` (×2) | Ideal | statevector | 20,000 | - |
522
- | `coherence_*_noisy_ibm_fez_*.json` (×2) | Noisy | ibm_fez noise | 20,000 | - |
523
- | `sim_*_statevector_*.json` | Ideal | statevector | 20,000 | - |
524
- | `sim_*_noisy_ibm_fez_*.json` | Noisy | ibm_fez noise | 20,000 | - |
525
 
526
- **Programmatic Loading:**
527
 
528
  ```python
529
  from datasets import load_dataset
530
- import pandas as pd
531
-
532
- # Load manifest
533
- ds = load_dataset("Cohaerence/ibm-qml-kernel", data_files="manifest/runs.csv")
534
- runs = pd.DataFrame(ds['train'])
535
-
536
- # Filter hardware runs
537
- hw_runs = runs[runs['run_type'] == 'hardware']
538
- print(hw_runs[['backend', 'mode', 'shots', 'job_id']])
539
 
540
- # Load specific result
541
- import json
542
- with open('artifacts/branch_transfer/hw_20260117_205401_ibm_fez_main_mu-1_shots-20000_opt-2.json') as f:
543
- result = json.load(f)
544
- print(f"Visibility: {result['visibility']:.4f} ± {result['visibility_error']:.4f}")
545
  ```
546
 
547
- **Verify File Integrity:**
548
- ```bash
549
- cd /path/to/dataset
550
- shasum -a 256 -c manifest/SHA256SUMS.txt
551
- # Expected: All files report "OK"
552
- ```
553
-
554
- **Original Bundle:**
555
- The ZIP file at `original/branch_transfer_arxiv_bundle_v2b.zip` preserves byte-for-byte parity with the arXiv submission bundle for archival compliance.
556
-
557
- ### Collapse / Nonunitary Channel Constraint Analysis
558
-
559
- **Method:**
560
- The protocol is used to constrain parameterized nonunitary channels (e.g., dephasing, amplitude damping) by:
561
- 1. Implementing the full protocol on ideal and noisy simulators
562
- 2. Comparing diagonal observables (visibility V) vs off-diagonal observables (coherence witnesses W_X, W_Y)
563
- 3. Sweeping a parameterized collapse channel (gamma parameter) and forecasting detectability against device noise
564
 
565
- **Analysis:**
566
- - **Visibility (V) is insensitive to dephasing**: Post-measurement dephasing in the Z-basis preserves diagonal populations, leaving V unchanged across all gamma values
567
- - **Coherence witnesses (W_X, W_Y) detect dephasing**: At gamma=0.05, the coherence deviation exceeds shot noise uncertainty (2-sigma threshold), while V remains unaffected
568
- - **Detectability threshold**: gamma ≈ 0.05 for coherence-based detection with 20k shots
569
 
570
- **Interpretation:**
571
- This analysis constrains specific parameterized channels (e.g., continuous spontaneous localization-style dephasing) by demonstrating that coherence-based observables provide complementary sensitivity beyond population measurements. **This does not prove or disprove Many-Worlds or any specific unitary interpretation**—it operationally constrains collapse-model parameter space within the measurement precision of current hardware.
572
 
573
- **Run the analysis:**
574
  ```bash
575
- # Coherence-based collapse model forecast (recommended for dephasing detection)
576
- python -m experiments.branch_transfer.collapse_models --mode coherence_witness --gamma-sweep --collapse-model dephase
577
 
578
- # Add backend-matched hardware noise
579
- python -m experiments.branch_transfer.collapse_models --mode coherence_witness --gamma-sweep --collapse-model dephase --add-hardware-noise
580
- ```
581
-
582
- ### Scaling Roadmap
583
 
584
- **Branch divergence scaling:**
585
- The protocol represents friend-0 and friend-1 measurement outcomes as orthogonal branches. To scale this:
586
 
587
- 1. **Increase branching complexity**: Represent friend outcomes as longer bitstrings (e.g., 2-qubit friend → 4 branches, 3-qubit friend → 8 branches)
588
- 2. **Swap complexity scaling**: The branch-swap operation (X-string on Q,R,F) generalizes to an X-string whose length scales with Hamming distance between branch labels
589
- 3. **Witness degradation analysis**: Measure how coherence witness fidelity (W_X, W_Y, C_magnitude) degrades as a function of:
590
- - Number of qubits in the swap operation
591
- - Circuit depth increase from additional branching
592
- - Hamming distance between swapped branches
593
 
594
- **Concrete example (implementable):**
595
- - Current: 1-qubit friend (2 branches), 3-qubit swap (X on Q,R,F)
596
- - Next: 2-qubit friend (4 branches), 4-5 qubit swap depending on branch pair
597
- - Analysis: Plot C_magnitude vs. (swap depth, Hamming distance, hardware noise level)
598
 
599
- This provides a concrete path to study how inter-branch communication degrades with system complexity and is directly implementable on current IBM hardware (up to ~10 qubits before depth/noise tradeoffs dominate).
600
 
601
- ---
602
 
603
- ## Roadmap
 
604
 
605
- - [ ] **Error mitigation**: Implement zero-noise extrapolation (ZNE) and probabilistic error cancellation (PEC)
606
- - [ ] **Scalability**: Extend to 4+ qubits with advanced feature maps
607
- - [ ] **Hardware runs**: Execute on IBM Brisbane/Kyoto with real queue submission
608
- - [ ] **Kernel alignment optimization**: Trainable feature map parameters
609
- - [ ] **Benchmarking**: Compare against classical kernels (RBF, polynomial) on standard datasets
610
- - [ ] **Branch-transfer scaling**: Implement multi-qubit friend register and measure witness degradation vs swap complexity
611
 
612
  ---
613
 
614
  ## References
615
 
616
- 1. Havlíček, V., et al. (2019). Supervised learning with quantum-enhanced feature spaces. *Nature*, 567(7747), 209–212. [DOI: 10.1038/s41586-019-0980-2](https://doi.org/10.1038/s41586-019-0980-2)
617
 
618
- 2. Schuld, M., & Killoran, N. (2019). Quantum machine learning in feature Hilbert spaces. *Physical Review Letters*, 122(4), 040504. [DOI: 10.1103/PhysRevLett.122.040504](https://doi.org/10.1103/PhysRevLett.122.040504)
619
 
620
- 3. IBM Quantum Documentation (2026). Hardware specifications for Eagle r3 processors. [quantum.ibm.com/docs](https://quantum.ibm.com/docs)
621
-
622
- 4. Temme, K., Bravyi, S., & Gambetta, J. M. (2017). Error mitigation for short-depth quantum circuits. *Physical Review Letters*, 119(18), 180509. [DOI: 10.1103/PhysRevLett.119.180509](https://doi.org/10.1103/PhysRevLett.119.180509)
623
-
624
- 5. Abbas, A., et al. (2021). The power of quantum neural networks. *Nature Computational Science*, 1(6), 403–409. [DOI: 10.1038/s43588-021-00084-1](https://doi.org/10.1038/s43588-021-00084-1)
625
-
626
- 6. Violaris, M. (2026). Quantum observers can communicate across multiverse branches. *arXiv:2601.08102*. [arXiv:2601.08102](https://arxiv.org/abs/2601.08102)
627
-
628
- ---
629
-
630
- ## Citations
631
-
632
- If you use this project in your research, please cite:
633
-
634
- ```bibtex
635
- @software{altman2026ibmqmlkernel,
636
- author = {Altman, Christopher},
637
- title = {Quantum Kernel Methods on IBM Quantum Hardware},
638
- year = {2026},
639
- url = {https://github.com/christopher-altman/ibm-qml-kernel},
640
- note = {Quantum kernel estimation with IBM hardware noise modeling and PSD projection}
641
- }
642
- ```
643
 
644
  ---
645
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
  ---
2
+ pretty_name: "IBM-QML-Kernel Branch-Transfer Benchmarks (wigner-friend-v2b)"
3
+ license: mit
4
+ tags:
5
+ - quantum-computing
6
+ - ibm-quantum
7
+ - qiskit
8
+ - superconducting-qubits
9
+ - reproducibility
10
+ - benchmarks
11
+ - wigners-friend
12
+ task_categories:
13
+ - other
14
+ size_categories:
15
+ - n<1K
 
 
 
 
16
  ---
17
 
18
+ # IBM-QML-Kernel Branch-Transfer Benchmarks (wigner-friend-v2b)
19
 
20
+ ## Dataset Summary
21
 
22
+ This dataset is the **reproducibility artifact bundle** corresponding to the arXiv submission:
 
 
 
 
23
 
24
+ **“Wigner's Friend as a Circuit: Inter-Branch Communication Witness Benchmarks on Superconducting Quantum Hardware.”**
25
+ GitHub release checkpoint: https://github.com/christopher-altman/ibm-qml-kernel/releases/tag/v1.0-wigner-branch-benchmark
26
+ Discussion / Hugging Face suggestion: https://github.com/christopher-altman/ibm-qml-kernel/issues/1
27
+ Paper page: https://huggingface.co/papers/2601.16004
28
 
29
+ It snapshots the experimental and simulation outputs for a **five‑qubit “branch‑transfer / message‑transfer” circuit primitive** (message transfer in the *compiled circuit / measurement record* sense, not physical signaling), executed on **IBM Quantum hardware** and mirrored with **backend‑matched noisy simulations**.
30
 
31
+ This Hugging Face dataset exists because Hugging Face surfaced the paper on Daily Papers and recommended hosting the artifacts here to improve discoverability and enable programmatic access + a dataset viewer.
 
 
 
32
 
33
+ ## What’s inside (high level)
34
 
35
+ The release is designed as a “stable, citeable checkpoint” and includes, at minimum:
36
 
37
+ - **Hardware execution** on IBM Quantum `ibm_fez` (N = 20,000 shots).
38
+ - **Coherence-sensitive witness evaluation** (X and Y bases) + a **visibility baseline**.
39
+ - **Backend-matched noisy simulations** using calibration-synchronized noise models.
40
+ - **Execution provenance**: IBM Quantum job IDs + backend calibration snapshots.
41
+ - **Deterministic figure regeneration** from archived artifacts.
42
+ - **Tamper-evident manifest**: SHA256 hashes for bundle files.
43
 
44
+ (See the GitHub release notes for the canonical inventory.)
45
 
46
+ ## Intended Use
 
 
 
 
47
 
48
+ This dataset is for:
49
 
50
+ - Reproducing figures/tables/values from the associated paper.
51
+ - Auditing compilation + noise impacts on the reported witnesses.
52
+ - Serving as a reference artifact for future “branch-transfer / inter-branch witness” benchmark runs on other devices/backends.
53
 
54
+ Not intended for: training NLP/Vision models. It’s an experiment + provenance bundle.
 
 
 
 
 
 
 
 
 
 
 
 
 
55
 
56
+ ## How to Use
57
 
58
+ ### Option A — download the full artifact snapshot (recommended for exact reproduction)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
59
 
60
+ For non-tabular artifacts (plots, calibration dumps, intermediate files), the most faithful workflow is to download the full repository snapshot:
61
 
62
+ ```python
63
+ from huggingface_hub import snapshot_download
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
64
 
65
+ local_dir = snapshot_download(
66
+ repo_id="Cohaerence/wigner-friend-v2b",
67
+ repo_type="dataset",
68
+ )
69
+ print(local_dir)
70
  ```
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
71
 
72
+ ### Option B `datasets.load_dataset(...)` (best if files are extracted + structured)
 
 
 
 
 
 
 
73
 
74
+ Hugging Face Datasets works best when the dataset includes common formats like `csv`, `jsonl`, or `parquet`, optionally referenced via `data_files=`.
75
 
76
  ```python
77
  from datasets import load_dataset
 
 
 
 
 
 
 
 
 
78
 
79
+ ds = load_dataset("Cohaerence/wigner-friend-v2b")
80
+ print(ds)
 
 
 
81
  ```
82
 
83
+ Docs: https://huggingface.co/docs/datasets/loading
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
84
 
85
+ ## Reproduction Quickstart (paper-aligned)
 
 
 
86
 
87
+ These commands reflect the intended “paper-aligned” reproduction workflow described in the release notes:
 
88
 
 
89
  ```bash
90
+ # Verify IBM Quantum connectivity
91
+ python -c "from qiskit_ibm_runtime import QiskitRuntimeService as S; s=S(); bs=s.backends(simulator=False, operational=True); print('n_backends=', len(bs))"
92
 
93
+ # Hardware coherence witness (X + Y bases)
94
+ python -m experiments.branch_transfer.run_ibm --backend ibm_fez --mode coherence_witness --include-y-basis --shots 20000 --optimization-level 2
 
 
 
95
 
96
+ # Hardware visibility (rp_z mode)
97
+ python -m experiments.branch_transfer.run_ibm --backend ibm_fez --mode rp_z --mu 1 --shots 20000 --optimization-level 2
98
 
99
+ # Backend-matched noisy simulations
100
+ python -m experiments.branch_transfer.run_sim --mode coherence_witness --include-y-basis --mu 1 --shots 20000 --noise-from-backend ibm_fez
101
+ python -m experiments.branch_transfer.run_sim --mode rp_z --mu 1 --shots 20000 --noise-from-backend ibm_fez
 
 
 
102
 
103
+ # Generate analysis figures
104
+ python -m experiments.branch_transfer.analyze --artifacts-dir artifacts/branch_transfer --figures-dir artifacts/branch_transfer/figures --plot-all
105
+ ```
 
106
 
 
107
 
108
+ ## Citations
109
 
110
+ - arXiv:2601.16004 — “Wigner's Friend as a Circuit: Inter-Branch Communication Witness Benchmarks on Superconducting Quantum Hardware.”
111
+ https://arxiv.org/abs/2601.16004
112
 
113
+ - Code + artifact checkpoint: GitHub release tag `v1.0-wigner-branch-benchmark`.
114
+ https://github.com/christopher-altman/ibm-qml-kernel/releases/tag/v1.0-wigner-branch-benchmark
 
 
 
 
115
 
116
  ---
117
 
118
  ## References
119
 
120
+ 1. Violaris, M. (2026). Quantum observers can communicate across multiverse branches. *arXiv:2601.08102*. [arXiv:2601.08102](https://arxiv.org/abs/2601.08102)
121
 
122
+ 2. Mukherjee, S. and Hance, J. Limits of absoluteness of observed events in timelike scenarios: A no-go theorem, *arXiv:2510.26562*. [arXiv:2510.26562](https://arxiv.org/abs/2510.26562)
123
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
124
 
125
  ---
126