DefinitionDefinition: Literature-sourcedProof: 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.

Symmetric second-order product formula

Definition

For the announced term order $1, \dots, m$ and real $h$ , define the palindromic product $S_{2} (h) : = e^{- i h H_{1} / 2} e^{- i h H_{2} / 2} \dots e^{- i h H_{m - 1} / 2} e^{- i h H_{m}} e^{- i h H_{m - 1} / 2} \dots e^{- i h H_{2} / 2} e^{- i h H_{1} / 2} .$ For $m = 1$ this is just $e^{- i h H_{1}}$ . The $r$ -step approximation is $S_{2} (t / r)^{r}$ , with $r \geq 1$ . A written product acts right-to-left, as in First-order Lie product formula. Every term call and any signed-time implementation cost must be declared by Term-list Hamiltonian access.

Depends on

Used by

Finite higher-order Suzuki product formula Algorithm
Suzuki recursive cancellation of error terms Lemma
Conservative second-order error Theorem

Dependency tree · two levels

10 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

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