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Record W4399107520 · doi:10.1016/j.bulsci.2024.103454

TQFTs and quantum computing

2024· article· fr· W4399107520 on OpenAlex
Mahmud Azam, Steven Rayan

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueBulletin des Sciences Mathématiques · 2024
Typearticle
Languagefr
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsUniversity of Saskatchewan
FundersNatural Sciences and Engineering Research Council of CanadaUniversities Space Research AssociationPacific Institute for the Mathematical Sciences
KeywordsFunctorCategorical variableSubcategoryConnection (principal bundle)MathematicsPure mathematicsQuantumVector spaceTopology (electrical circuits)Quantum mechanicsGeometryCombinatoricsPhysics

Abstract

fetched live from OpenAlex

Quantum computing is captured in the formalism of the monoidal subcategory of Vect C generated by C 2 — in particular, quantum circuits are diagrams in Vect C — while topological quantum field theories , in the sense of Atiyah, are diagrams in Vect C indexed by cobordisms. We initiate a program to formalize this connection. In doing so, we equip cobordisms with machinery for producing linear maps by parallel transport along curves under a connection and then assemble these structures into a higher category. Finite-dimensional complex vector spaces and linear maps between them are given a suitable higher categorical structure which we call F Vect C . We realize quantum circuits as images of cobordisms under monoidal functors from these modified cobordisms to F Vect C , which are computed by taking parallel transports of vectors and then combining the results in a pattern encoded in the domain category.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.003
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Insufficient payload (model declined to judge)
Consensus categoriesInsufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.153
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0030.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.000
Science and technology studies0.0010.008
Scholarly communication0.0010.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.001

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.

Opus teacher head0.050
GPT teacher head0.338
Teacher spread0.289 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it