State
Nonlinear initial-value problem
A nonlinear vector field F, an initial condition, a time to evolve to, and an error you are willing to accept. Nothing quantum acts on this directly — quantum time evolution is linear — so every route begins by changing what it is holding.
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
- Solve a nonlinear ODE dy/dt = F(y)
Given access to a nonlinear vector field — in practice quadratic or polynomial — and a preparation unitary for the initial state, produce a quantum state proportional to or an estimate of an observable of it. Quantum time evolution is linear, so no quantum primitive acts on this contract directly.
- Embed a nonlinear system into a linear one
Given a nonlinear vector field , produce a (truncated) linear generator on a lifted space, a lift of the initial condition into that space, and a decoding of the target quantity, such that linear evolution reproduces the nonlinear dynamics to accuracy . The truncation or lift parameter fixes both the accuracy and the dimension.