Every record is classified by how it was verified. The badge shows the strongest tier of evidence; the chips list each method that applies.
≡Exact & formalThe defining behavior was checked exactly: a mathematical identity, a full statevector or stabilizer simulation, or an exhaustive basis-state truth table.
- Direct mathematics
- An analytic identity or closed-form derivation proves the defining property (e.g. H² = I, Y = iXZ).
- Unitary / matrix equivalence
- The circuit's unitary was computed and compared against the reference matrix.
- Exact statevector simulation
- A full statevector simulation reproduced the exact expected state or distribution.
- Stabilizer simulation
- Clifford structure allowed exact verification with stabilizer methods beyond statevector limits.
- Basis-state truth table
- Reversible classical logic was checked exhaustively (or at edge cases) on computational-basis inputs.
✓Strong empiricalThe design was verified by construction plus measured evidence: statistical re-execution, small-instance analytic agreement, sub-block, echo, or invariant checks. Scale-specific bugs can still survive.
- Statistical re-execution
- Measured counts from independent executions agreed within statistical tolerance (e.g. TVD bounds).
- Small-instance agreement
- The same generator matched analytic results at tractable sizes; large instances are inferred.
- Sub-block verification
- Reusable modules (oracle, QFT block, Trotter step, adder…) were verified independently.
- Echo / inverse test
- U followed by U† returned the input exactly, catching wiring, phase, and ancilla bugs.
- Invariant & structural checks
- Scale-independent invariants held: qubit counts, unitarity, symmetry, conservation laws, ancilla cleanup.
- Verified by construction
- The circuit follows a specification whose correctness argument is standard; the construction was audited against it.
◐Attested & literatureThe record rests on external authority: peer-reviewed papers, standard textbooks, expert review, or evidence carried over from related verified entries. Nothing here was re-executed by this catalog.
- Peer-reviewed paper
- The record's claims trace to one or more peer-reviewed publications cited on the entry.
- Textbook / standard citation
- The behavior is standard material (e.g. Nielsen & Chuang, OpenQASM spec) and is cross-referenced, not re-derived.
- Expert review
- A named human reviewer with domain expertise checked the record.
- Tangential evidence
- Correctness is supported indirectly through related verified entries (e.g. a gate verified inside a verified algorithm).
- LLM-assisted review
- An LLM checked the record for internal consistency. Useful screening, not evidence of correctness.
- Community submission
- Submitted by the community and not yet through the review pipeline.