Pauli-based model of quantum computation with higher-dimensional systems
Bibliographic record
Abstract
Pauli-based computation (PBC) is a universal model for quantum computation with qubits where the input state is a magic (resource) state and the computation is driven by a sequence of adaptively chosen and compatible multiqubit Pauli measurements. Here we generalize PBC for odd-prime-dimensional systems and demonstrate its universality. Additionally, we discuss how any qudit-based PBC can be implemented on actual, circuit-based quantum hardware. Our results show that we can translate a PBC on $n\phantom{\rule{4pt}{0ex}}p$-dimensional qudits to adaptive circuits on $n+1$ qudits with $O\left(p{n}^{2}/2\right)$ sum gates and depth. Alternatively, we can carry out the same computation with $O\left(pn/2\right)$ depth at the expense of an increased circuit width. Finally, we show that the sampling complexity associated with simulating a number $k$ of virtual qudits is related to the robustness of magic of the input states. Computation of this magic monotone for qutrit and ququint states leads to sampling complexity upper bounds of, respectively, $O({3}^{1.0848k}{\ensuremath{\epsilon}}^{\ensuremath{-}2})$ and $O({5}^{1.4022k}{\ensuremath{\epsilon}}^{\ensuremath{-}2})$, for a desired precision $\ensuremath{\epsilon}$. We further establish lower bounds to this sampling complexity for qubits, qutrits, and ququints: $\mathrm{\ensuremath{\Omega}}({2}^{0.5431k}{\ensuremath{\epsilon}}^{\ensuremath{-}2})$, $\mathrm{\ensuremath{\Omega}}({3}^{0.7236k}{\ensuremath{\epsilon}}^{\ensuremath{-}2})$, and $\mathrm{\ensuremath{\Omega}}({5}^{0.8544k}{\ensuremath{\epsilon}}^{\ensuremath{-}2})$, respectively.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".