--- 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. ![Pulse-budget rank at seven bins](research/figures/rank_staircase.png) 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. ![A deeper control separates shallow-indistinguishable laws](research/figures/dark_revelation.png) ### 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/.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.