State

Answer about the solution

Whatever a route hands back about the state of the system at the end — a state you can measure, a history over the whole interval, or a single number. Which of the three you get is a real difference between routes, so each is its own kind below this one.

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

Solution as a state
A normalised quantum state close to the answer vector. You can measure it and you can feed it onward, but you do not have its norm, any one of its entries, or any classical function of it — those cost extra and are decided a layer up.
History state
The solution at every recorded time step, superposed in one register with a clock. Reading one time out of it costs a measurement that lands on the others too.
Number with an error bar
A scalar estimate with an additive-error guarantee, the shot or query budget it consumed, and the deepest circuit it actually ran. Every claim about an application eventually has to arrive here.

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

Solve a nonlinear ODE dy/dt = F(y)
Given access to a nonlinear vector field $F$ — in practice quadratic or polynomial — and a preparation unitary for the initial state, produce a quantum state proportional to $y(T)$ or an estimate of an observable of it. Quantum time evolution is linear, so no quantum primitive acts on this contract directly.
Solve a linear ODE du/dt = A(t)u + b(t)
Given block-encoding access to $A(t)$ and $b(t)$ and a preparation unitary for $u_0$ , output a normalized state $\varepsilon$ -close to $u(T)/||u(T)||$ . Matrix-query and state-preparation-query counts are stated separately, because methods here differ in them independently.

Work that starts here

No recorded process takes this as its input. Nothing in this graph leaves from here.