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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.
![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/<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.