A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics
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Bibliographic record
Abstract
We introduce the first complete and approximatively universal diagrammatic\nlanguage for quantum mechanics. We make the ZX-Calculus, a diagrammatic\nlanguage introduced by Coecke and Duncan, complete for the so-called Clifford+T\nquantum mechanics by adding four new axioms to the language. The completeness\nof the ZX-Calculus for Clifford+T quantum mechanics was one of the main open\nquestions in categorical quantum mechanics. We prove the completeness of the\nClifford+T fragment of the ZX-Calculus using the recently studied ZW-Calculus,\na calculus dealing with integer matrices. We also prove that the Clifford+T\nfragment of the ZX-Calculus represents exactly all the matrices over some\nfinite dimensional extension of the ring of dyadic rationals.\n
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| 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 it