DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated

How 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.

Quantum query complexity

Definition

For a $T$ -query quantum algorithm Quantum query algorithm at input length $n$ , its worst-case quantum query cost is the maximum number of designated oracle calls over all promised instances in $P_{n}$ and all measurement branches. When $P_{n}$ is empty, define this cost to be $0$ . For nonempty $P_{n}$ , a finite circuit and finite branch sets ensure that this maximum exists; a solver whose branch counts are not uniformly bounded has infinite worst-case query cost. An expected-query bound is the separate quantity defined by Expected query cost from finite execution prefixes.

In the pure query model, ordinary gates outside the oracle calls are uncharged by the query coordinate. If a task also reports gate, preparation, measurement, or classical costs, those are separate coordinates. Bounded-error query cost uses the same worst-case maximum; its success threshold is the per-instance condition in Worst-case bounded-error correctness, not an average over oracle inputs.

Depends on

Used by

Boolean oracle query model for search lower bounds Definition
Finite Boolean query problem and error model for adversary bounds Definition
Promise, query and cost-model examples Example
Amplitude-amplification access and resource accounting Proposition
Amplitude-estimation query and precision complexity Theorem
Arbitrary-phase amplification query count Theorem
BBBV hybrid lower bound for unstructured search Theorem
Bounded-error unstructured search query complexity is Theta of square root N Theorem
Controlled consistency reflection uses two bit queries Theorem
Dual reflection evaluator query complexity Theorem
Exact query count for the finite-grid iterative estimator Theorem
Exact-success amplitude amplification query cost Theorem
Expected bit-query cost of unknown-count BBHT search Theorem
Expected cost of unknown-amplitude search Theorem
Fixed-round amplitude amplification query count Theorem
General adversary bound characterizes Boolean quantum query complexity Theorem
General adversary spectral lower bound for quantum queries Theorem
Grover search upper-bound query cost Theorem
Known-amplitude amplification query cost Theorem
Known-count Grover search uses O of the square root of N over t bit queries Theorem
Median amplitude-estimation query cost Theorem
One Grover iterate uses one standard bit query Theorem
Promise-preserving reduction composes with a query solver Theorem
Quantum counting query complexity Theorem
Query cost of randomized known-count Grover search Theorem
Relative approximate counting query complexity Theorem

Dependency tree · two levels

21 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

Ronald de Wolf, Quantum Computing: Lecture Notes (standard reference, not scraped)
Andrew M. Childs, Lecture Notes on Quantum Algorithms (standard reference, not scraped)
John Preskill, Quantum Information, Chapter 6: Quantum Algorithms (standard reference, not scraped)