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 & formal
The 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.
Reversible classical logic was checked exhaustively (or at edge cases) on computational-basis inputs.
✓Strong empirical
The 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.
The circuit follows a specification whose correctness argument is standard; the construction was audited against it.
◐Attested & literature
The 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).
○Automated & unreviewed
Only automated (LLM-assisted) review or an unreviewed community submission backs this record so far. Treat it as a starting point, not evidence.
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.
267 entries · 284 records, sized variants folded
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Let G be a finitely generated Abelian group and let H be a subgroup of G such that G/H is finite, and let f be a function on G with the promise that f(g1) = f(g2) if and only if g1 and g2 lie in the same coset of H. The task is to find H, that is, a set of generators for H, by making queries to f. Mosca and Ekert work order finding and period finding as G = Z with hidden subgroup rZ, Simon's problem as G = Z_2^l, and the discrete logarithm as G = Z_r × Z_r.
Find a better parameterized ansatz for the quantum approximate optimization algorithm (QAOA) applied to combinatorial optimization problems such as Max-Cut, where the standard, fixed-form QAOA ansatz is not known to be optimal and no systematic method exists for improving on it.
Give polynomial-time quantum algorithms for three average-case lattice problems in parameter regimes where none was known: the short integer solution problem under the infinity norm, the learning-with-errors problem when the input is supplied as LWE-like quantum states rather than classical samples, and the extrapolated dihedral coset problem.
lattice problemslearning with errorsshort integer solution
Backtracking is the general classical technique for exploiting problem structure in constraint satisfaction: explore a tree of partial assignments and prune the branches a predicate rules out. The question is whether an arbitrary backtracking algorithm — any predicate and any branching heuristic — can be sped up quantumly, rather than replaced by brute-force search over the whole assignment space.