DefinitionDefinition: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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.

Big-endian encoding of ordered bit strings

Definition

For $n \geq 0$ and a binary word $x = (x_{0}, \dots, x_{n - 1}) \in {0, 1}^{n}$ , define its big-endian index

${enc}_{n} (x) : = \sum_{k < n} x_{k} 2^{n - 1 - k} .$

Thus the first wire is the most significant bit. For $n = 0$ , the domain ${0, 1}^{0}$ consists only of the empty word $()$ , and the empty sum gives ${enc}_{0} (()) = 0$ . In an ordered $n$ -qubit computational basis, the word $x$ occupies the slot numbered ${enc}_{n} (x)$ .

Depends on

Finite registers and their ordered computational bases

Used by

Costed coherent evaluation of cyclic group powers Algorithm
Exact binary QFT circuit Algorithm
Exact Two-Level Elimination of a Unitary Algorithm
Gray-Path Synthesis of a Two-Level Gate Algorithm
Isometry Unitary Completion Algorithm
One finite abelian hidden-subgroup Fourier sample Algorithm
One-query Bernstein–Vazirani algorithm Algorithm
One-query Deutsch algorithm Algorithm
One-query Deutsch–Jozsa algorithm Algorithm
Power-of-two dihedral hidden-subgroup sieve Algorithm
QC24 State Preparation Algorithm
Quantum phase estimation Algorithm
Reversible embedding of a Boolean circuit Algorithm
Reversible modular multiplication by a unit Algorithm
Reversible zero-completion of an N-address bit query Algorithm
Binary adjacency matrix of an ordered finite simple graph Definition
Binary phase-query convention Definition
Coherent XOR function oracle Definition
Eigenphase estimation access model Definition
Finite abelian hidden-shift promise Definition
Finite abelian hidden-subgroup promise and output encoding Definition
Finite circuit syntax and ordered wire labels Definition
Finite cyclic discrete-logarithm problem and costed encoding Definition
Finite marked-item search and its bit oracle Definition
Finite quantum promise-computation model Definition
Graph state of an ordered finite simple graph Definition
Oracle-only bit-query algorithm Definition
Phase aware n qubit pauli group Definition
Phase-aware binary Clifford tableau Definition
Promise query instance and oracle family Definition
QC24 State Preparation Cost Model Definition
Simon injectivity decision promise with XOR-oracle access Definition
Standard bit-flip query convention Definition
Toffoli and Fredkin gates Definition
Two-Level Unitary Definition
A reversible AND oracle with clean work Example
Register endianness and a two-qubit partial trace Example
Binary factorization of QFT basis output Lemma
Clean reversible controlled multiplication by a cyclic constant Lemma
Computational basis states have an extended stabilizer tableau Lemma

…and 22 more results.

Dependency tree · two levels

9 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

John Watrous, The Theory of Quantum Information (standard reference, not scraped)
Ronald de Wolf, Quantum Computing: Lecture Notes (standard reference, not scraped)