Data and code for "Freeness Reined in by a Single Qubit"
Bibliographic record
Abstract
Abstract Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework under a minimal deviation from freeness: the coupling of a single ancilla qubit to a Haar-distributed quantum circuit of dimension $D_0\gg 1$. We find that, even in this setting, the correlation functions predicted by free probability theory receive corrections of order $O(1)$. These modifications persist at long times, when the dynamics of the coupled system is already ergodic. We trace their origin to non-uniformly distributed stationary quantum states, which we characterize analytically and confirm numerically. Data and code for Freeness Reined in by a Single Qubit Here, we provide the numerical code and precomputed Monte-Carlo data used to reproduce the spectral form factor (SFF) and two-point correlation function (CBA) figures in the companion manuscript "Freeness Reined in by a Single Qubit." The repository includes Precomputed Monte-Carlo data Spectral form factor data: estimates of $\overline{|⟨U^t⟩|²}$ for discrete times $t = 1,\dots,300$. Two-point correlator ("CBA") data: values of $\overline{⟨A B(t)⟩}$ stored as a complex array (the plots use the real part). Results are provided for multiple ancilla-environment coupling strengths $g \in \{0.5,\,0.6,\,0.8,\,1.0\}$, internally mapped to the rate $\gamma = g^{2}/2$. Default model size: an environment register of $6$ qubits plus one ancilla qubit, yielding a total Hilbert-space dimension $D = 128$. The numerics are performed using Python code included in the repository. A Jupyter notebook loads the data and reproduces all plots in publication-ready form. Files 01\_sff\_cba.py: Monte-Carlo simulation script (generates Data/*.pkl) 02\_plots.ipynb: plotting notebook (loads Data/*.pkl and generates figures) Data/: precomputed dataset sff\_cba\_multi\_g\_env6\_samples1000000.pkl Results/: output figures produced by the notebook: SFF\_multig\_env6\_samples1000000.(pdf|png) CBA\_env6\_samples1000000.(pdf|png) The Jupyter notebook automatically loads the data stored in the folder Data/ and writes the resulting figures to Results/.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".