Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Basic Clifford T Rewrite
Definition
Input is a finite word of H,T,T†,CNOT gates with ordered wire labels. Fix the rules H²→ε, T⁸→ε, TT†→ε, T†T→ε, and CNOT²→ε, where ε means the empty subword; apply the cancellation rules only when the adjacent gates have the same ordered support. Scan left-to-right, choose the first match, delete the matched subword, restart the scan, and halt when no rule matches. Empty words are permitted. The output remains a word over the input gate alphabet and is locally irreducible for this displayed rule set; it makes no global-minimum claim.
The gate labels use the exact matrices and ordered supports fixed by Clifford+T gate library and exact matrices.
Depends on
Used by
Dependency tree · two levels
6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Barenco et al., Elementary gates for quantum computation (standard reference, not scraped)
- Andrew M. Childs, Lecture Notes on Quantum Algorithms (standard reference, not scraped)