AlgorithmAlgorithm: 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.

Median confidence amplification for amplitude estimation

Definition

Input. The amplitude-estimation task, rational $0 < ϵ \leq 1$ and rational $0 < δ < 1$ .

Initialize $m = 0$ and $M = 1$ . Repeatedly increment $m$ and double $M$ while $M < 88 / (7 ϵ)$ , using exact rational comparison, so that $M = 2^{m}$ . Set $r = 1$ and repeatedly increase $r$ by $2$ while $2^{r} < (2 / δ)^{8}$ , using exact rational comparisons. Run $r$ independent fresh copies of the QFT estimator with phase-register size $M$ , and return the middle order statistic of their exact algebraic estimates (ties are ordered by their exact value and identical values are interchangeable).

Depends on

Used by

Amplitude-estimation expectation estimator Algorithm
Explicit median confidence guarantee for amplitude estimation Theorem
Median amplitude-estimation query cost Theorem
Quantum bounded-expectation guarantee and query cost Theorem

Dependency tree · two levels

55 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

Brassard, Høyer, Mosca, and Tapp, Quantum Amplitude Amplification and Estimation, complete article, §§4–5, Theorems 11–18 (standard reference, not scraped)
Andrew M. Childs, Lecture Notes on Quantum Algorithms, complete lecture notes, §§19.1–19.3 (standard reference, not scraped)
Ronald de Wolf, Quantum Computing: Lecture Notes, complete 239-page notes, §7.3 (standard reference, not scraped)