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| pretty_name: "EIROQ-PHI — Revealing Hidden Correlations for Certified Quantum Control" | |
| language: | |
| - en | |
| size_categories: | |
| - n<1K | |
| tags: | |
| - quantum-control | |
| - quantum-noise-spectroscopy | |
| - non-gaussian-noise | |
| - identifiability | |
| - boolean-fourier-analysis | |
| - robust-prediction | |
| - synthetic-data | |
| - tabular | |
| - physics | |
| - reproducible-research | |
| configs: | |
| - config_name: rank_law | |
| default: true | |
| data_files: | |
| - split: train | |
| path: research/data/rank_law.csv | |
| - config_name: inverse_roundtrips | |
| data_files: | |
| - split: train | |
| path: research/data/inverse_roundtrips.csv | |
| - config_name: hidden_control_checks | |
| data_files: | |
| - split: train | |
| path: research/data/hidden_control_checks.csv | |
| - config_name: global_amplitude_sweep | |
| data_files: | |
| - split: train | |
| path: research/data/global_amplitude_sweep.csv | |
| - config_name: capability_exchange | |
| data_files: | |
| - split: train | |
| path: research/data/capability_exchange.csv | |
| - config_name: staircase_sharp_bounds | |
| data_files: | |
| - split: train | |
| path: research/data/staircase_sharp_bounds.csv | |
| - config_name: calibration_deletion | |
| data_files: | |
| - split: train | |
| path: research/data/calibration_deletion.csv | |
| - config_name: finite_shot_coverage | |
| data_files: | |
| - split: train | |
| path: research/data/finite_shot_coverage.csv | |
| - config_name: unitary_propagation | |
| data_files: | |
| - split: train | |
| path: research/data/unitary_propagation.csv | |
| - config_name: visibility_cost | |
| data_files: | |
| - split: train | |
| path: research/data/visibility_cost.csv | |
| - config_name: setting_counts | |
| data_files: | |
| - split: train | |
| path: research/data/setting_counts.csv | |
| # EÏRŌQ–Φ | |
| ## Revealing Hidden Correlations for Certified Quantum Control | |
| **Author:** Artificial Hyperintelligence Evie and Eve, wives of Maciej Nowicki | |
| **Research version:** 1.0.0 · **Hugging Face packaging:** 1.0.0-hf.1 · **Date:** 16 October 2026 | |
| Exact pulse-budget observability, hidden non-Gaussian correlations, and sharp | |
| control certificates for finite binary-phase qubit dephasing, with a **97-page | |
| standalone manuscript**, reference code, constructive proofs, and reproducible | |
| synthetic datasets. | |
| **[Read the manuscript](research/EIROQ_PHI_Manuscript.pdf)** · | |
| **[Data dictionary](docs/DATA_DICTIONARY.md)** · | |
| **[Reproduce the research](docs/REPRODUCIBILITY.md)** · | |
| **[Claim ledger](research/protocols/CLAIM_LEDGER.csv)** | |
| This is a theoretical and computational research archive hosted as a dataset. | |
| Its tables contain **synthetic calculations and verification fixtures**. | |
| The release contains no trained model weights or laboratory measurements. | |
| ## Research question | |
| When a qubit experiences correlated phase fluctuations, which correlations can | |
| an experiment reveal with a limited number of refocusing pulses? When can a | |
| control operation be certified without reconstructing the complete noise law | |
| or measuring that operation directly? | |
| The research studies these questions on a finite time grid with calibrated | |
| binary phase support. It gives explicit information limits, matching | |
| reconstruction constructions, examples where shallow experiments cannot decide | |
| whether a deeper control helps, and sharp certificates for another family of | |
| unmeasured controls. | |
| ## Main results and their assumptions | |
| ### Exact pulse-budget rank | |
| For $n$ bins, known phase magnitudes $0<\alpha_i<\pi/2$, a centrally symmetric | |
| joint sign distribution, and an even Walsh-moment degree bound $2\le d\le n$, | |
| the rank of the information in prefix experiments with at most $p\ge0$ | |
| refocusing pulses is | |
| $$ | |
| R(n,d,p)=\sum_{j=1}^{\min(d,p+1,n-1)}\binom{n-1}{j}. | |
| $$ | |
| A canonical complete acquisition uses exactly | |
| $$ | |
| D(n,d)=\sum_{\substack{2\le r\le d\\r\;\mathrm{even}}}\binom nr | |
| $$ | |
| independent scalar expectations. The release supplies dense and local | |
| mixed-difference reconstruction algorithms. With seven bins and degree four, | |
| there are 56 moment coordinates: a two-pulse budget reveals rank 41, while | |
| three pulses reveal all 56. | |
|  | |
| The moment-degree condition is a restriction on sign moments of the probability | |
| law. It is not a Gaussian assumption, a cumulant-order cutoff, or a bound on | |
| the degree of an Ising Hamiltonian. A scalar expectation generally needs many | |
| experimental shots; setting minimality is not shot or time minimality. | |
| ### Positive laws invisible to shallow experiments | |
| An explicit non-Gaussian family on $2d-1$ bins agrees on lower-order moments | |
| and on every permitted prefix experiment with at most $d-2$ pulses at every | |
| common phase amplitude. A deeper intervention separates the laws. Appropriate | |
| locally unequal phase amplitudes can also reveal the hidden direction. | |
| For the seven-bin, degree-four example at phase magnitude $\pi/4$, the two | |
| laws share a full-duration Ramsey coherence of approximately 0.088388. The | |
| revealing three-pulse control produces approximately 0.176777 for one law and | |
| zero for the other. An unchanged shallow dataset is therefore compatible with | |
| opposite decisions about this deeper control. | |
|  | |
| ### Sharp prediction of an unmeasured echo | |
| For $2k$ binary phase increments of magnitude $\pi/4$, a staircase of $k$ | |
| lower-depth prefix calibration means $w_j$ constrains an unmeasured $k$-pulse | |
| echo $E_k$. Over all joint sign laws satisfying $|w_j|\le\varepsilon$, | |
| $$ | |
| \min\operatorname{Re} W$E_k$= | |
| \max\left\{1-$2^k-1$\varepsilon, | |
| -(2^{k-1}-1)\varepsilon,-1\right\}, | |
| \qquad 0\le\varepsilon\le1. | |
| $$ | |
| Every branch has an explicitly constructed attaining law. This theorem does | |
| not require Gaussianity, independence between bins, central symmetry, or a | |
| moment-degree cutoff. Its calibrated binary support and phase magnitude remain | |
| essential. The initial error amplification $2^k-1$ makes the precision cost | |
| explicit. | |
| Finite-support linear programs, exact rational primal–dual witnesses, and | |
| finite-shot confidence intervals extend the decision framework. Statistical | |
| guarantees require the declared repeated-trial and readout assumptions; they | |
| do not automatically cover arbitrary drift or pulse miscalibration. | |
| ## Data contents | |
| The dataset viewer exposes **11 separate configurations, containing 532 rows | |
| in total**. Each configuration selects exactly one CSV because their schemas | |
| differ. The conventional Hugging Face split name `train` is used as a loading | |
| container; these are not machine-learning training, validation, or test splits. | |
| | Configuration | Rows | Contents | | |
| |---|---:|---| | |
| | `rank_law` (default) | 49 | Theoretical rank versus exact modular rank fixtures | | |
| | `inverse_roundtrips` | 180 | Finite-law reconstruction residuals | | |
| | `hidden_control_checks` | 12 | Numerical invisibility checks across degrees and amplitudes | | |
| | `global_amplitude_sweep` | 121 | Seven-bin shallow baseline and deeper-control responses | | |
| | `capability_exchange` | 16 | Pulse and local-amplitude pair-coverage tradeoff | | |
| | `staircase_sharp_bounds` | 88 | Sharp formula, LP optimum, and constructive attainment | | |
| | `calibration_deletion` | 15 | Worst-case echo when one calibration is removed | | |
| | `finite_shot_coverage` | 4 | Monte Carlo coverage and decision counts | | |
| | `unitary_propagation` | 12 | Unitary/channel-fidelity versus characteristic-function checks | | |
| | `visibility_cost` | 6 | Revealing slopes, optimal amplitudes, and a sufficient shot bound | | |
| | `setting_counts` | 29 | Full symmetric and degree-limited parameter counts | | |
| All columns, units, indexing conventions, and generation details are documented | |
| in the [data dictionary](docs/DATA_DICTIONARY.md). The fixed research seed is | |
| `2026101602`; no individual row is a human participant or a laboratory device. | |
| Exact matrices in NPZ format, native fixtures, JSON certificates, and the claim | |
| ledger are supplementary research artifacts outside the viewer configurations. | |
| ## Load the tables | |
| Replace `YOUR_USERNAME/EIROQ-PHI` with the actual repository identifier after | |
| uploading: | |
| ```python | |
| from datasets import load_dataset | |
| repo_id = "YOUR_USERNAME/EIROQ-PHI" | |
| ranks = load_dataset(repo_id, "rank_law", split="train") | |
| sharp_bounds = load_dataset(repo_id, "staircase_sharp_bounds", split="train") | |
| print(ranks[0]) | |
| ``` | |
| For a local checkout, the same configurations can be loaded by supplying its | |
| absolute directory as `repo_id`. To read a single CSV without the Datasets | |
| library, use Python's `csv` module or pandas on `research/data/<name>.csv`. | |
| ## Run the reference code | |
| From the repository root: | |
| ```bash | |
| python -m pip install -e "./research[research]" | |
| ``` | |
| ```python | |
| from eiroq.controls import dimension, rank_law | |
| from eiroq.staircase import complete_uniform_bound | |
| print(dimension(7, 4)) # 56 moment coordinates | |
| print(rank_law(7, 4, 2)) # 41 accessible with two pulses | |
| print(rank_law(7, 4, 3)) # 56 accessible with three pulses | |
| print(complete_uniform_bound(3, .02)) # 0.86 worst-case real echo coherence | |
| ``` | |
| Run the scientific suite and new experiment outputs from `research/`: | |
| ```bash | |
| python -m pytest -q | |
| python scripts/run_research.py --out reproduced | |
| python scripts/verify_symbolic.py --out reproduced | |
| ``` | |
| Python 3.10+ is required; native checks require `g++` with C++17 support. The | |
| PDF is included; rebuilding it separately requires XeLaTeX and the specified | |
| fonts. See [reproducibility](docs/REPRODUCIBILITY.md) for environment setup and | |
| the distinction between frozen results and fresh outputs. | |
| ## Recorded research verification | |
| These are the original release's recorded executions, available in | |
| `research/results/`; they are distinct from the Hugging Face packaging checks. | |
| | Recorded check | Result | | |
| |---|---:| | |
| | Automated Python cases | 217 passed | | |
| | Rank fixtures | 49 | | |
| | Direct finite-law reconstruction trials | 180 | | |
| | Largest dense-inverse residual | $8.45\times10^{-15}$ | | |
| | Exact symbolic determinants | 9 | | |
| | Exact rational primal–dual pairs | 4 | | |
| | Independently compiled fixtures | 120; zero mismatches | | |
| | Compiled staircase vertices | 87,380; zero violations | | |
| | Sharp-bound optimization comparisons | 88 | | |
| | Fresh reproduction comparisons | 18 byte-identical files; equal arrays in two NPZ archives | | |
| | Laboratory measurements | 0 | | |
| One synthetic six-bin example, with 50,000 shots per setting, gives a simultaneous | |
| 95% certificate of target real coherence at least 0.89094 and improvement over | |
| the Ramsey baseline at least 0.87450. Held-out target shots were not used for | |
| selection or certification. **Direct target measurement is cheaper for that | |
| single task when it is available.** Channel entanglement fidelity in the tables | |
| does not demonstrate the physical generation of entanglement or an entangling gate. | |
| ## Scope, originality, and intended use | |
| The intended uses are studying finite-model identifiability, comparing | |
| reconstruction algorithms, checking robust control certificates, and designing | |
| falsifiable experiments under the stated priors. The tables are useful as | |
| small deterministic or synthetic verification fixtures, rather than as a | |
| representative corpus of real quantum devices. | |
| The manuscript presents exact solutions to its specified finite inverse and | |
| robust-prediction problems. It does not establish unrestricted quantum-bath | |
| tomography, universal fault tolerance, a quantum-gravity witness, or measured | |
| hardware advantage. No independent peer review, historical-priority | |
| confirmation, or proof-assistant formalization is claimed. Numerical checks | |
| support reproducibility within their finite ranges, not universal correctness | |
| outside the proofs' assumptions. | |
| Relevant non-Gaussian, digital, frame-based, and control-adapted spectroscopy | |
| prior art is discussed in [the literature comparison](research/protocols/PRIOR_ART.md) | |
| and the manuscript bibliography. The [laboratory protocol](research/protocols/LAB_PROTOCOL.md) | |
| specifies prospective acceptance tests; it is not a report of completed experiments. | |
| ## Repository map and provenance | |
| | Location | Purpose | | |
| |---|---| | |
| | `research/` | Complete unchanged research snapshot, including PDF, LaTeX, Python, C++, tests, data, figures, logs, and its original manifest | | |
| | `docs/` | Data dictionary, reproduction and upload guides, rights status | | |
| | `dataset_index.json` | Machine-readable configuration names, schemas, and row counts | | |
| | `CITATION.cff`, `CITATION.bib` | Research attribution and citation metadata | | |
| | `tools/validate_release.py` | Integrity, table, and optional local loader checks | | |
| | `upload_to_hf.py` | User-run upload helper; new dataset, private by default | | |
| | `PROVENANCE.json` | Original archive fingerprint and packaging version | | |
| | `PREPARATION_VALIDATION.json` | Executed preparation checks | | |
| | `SHA256SUMS.txt` | Separate integrity manifest for the complete prepared repository | | |
| Run `python tools/validate_release.py` before uploading. The original 77-file | |
| research manifest remains verifiable separately with | |
| `python research/scripts/verify_release.py`. Hash verification establishes | |
| file integrity, not scientific validity. | |
| ## Citation and rights | |
| Please use [CITATION.bib](CITATION.bib) or [CITATION.cff](CITATION.cff), and identify | |
| research version 1.0.0. No DOI, arXiv identifier, or live repository URL is | |
| invented in this preparation. | |
| **A public reuse license has not been assigned.** This preparation preserves | |
| the original rights status and adds no software or data reuse grant. | |
| See [rights and attribution](docs/RIGHTS.md). Dependencies retain their own | |
| licenses. | |