State
Function promised to be periodic
A function you can evaluate on a superposition of inputs, together with the promise that it repeats — and, decisively, the kind of thing its period is allowed to be. An integer in a finite cyclic group, an irrational real, or a lattice of periods in several dimensions are three different promises, and the routes that answer them are not interchangeable.
A state is an object you can be holding, named once so that two routes reaching the same thing are drawn as reaching the same thing. It says nothing about how you got here or where you can go next — that is entirely in the processes below.
This is a kind of
This state is not recorded as a kind of anything else. It stands on its own in the vocabulary.
Narrower kinds of this
No state in the vocabulary is recorded as a narrower kind of this one.
Records that are this object
Nothing in the catalogue has been joined to this state. That is a gap in the join rather than a claim that no such object exists; the shelf on /repository lists what is joined and what is not, with the reason.
Work that arrives here
No recorded process returns this. Either it is where a reader starts — a problem, a matrix, a machine — or it is an object this graph names and no route yet reaches.
Work that starts here
- Recover the period of a periodic function
Given a function you can evaluate in superposition and a promise that it repeats, find what it repeats by. This is the engine underneath factoring, discrete logarithms and a row of classical number-theory problems that had no efficient algorithm at all — and the whole difficulty is that the period is read out of an interference pattern rather than looked up.