State

State you can prepare

Not the state itself but the routine that makes it — which is the useful form, because a routine can be run again, controlled, and inverted, and a state that has already collapsed can do none of those.

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.
Reliable routine
The same routine after the good branch has been amplified, now carrying a failure probability you can quote, a query count, and the sequential depth that buying the reliability consumed.
Evolution circuit, input in hand
An evolution circuit together with the preparation routine for the input it acts on. The pair is still a circuit — its error and its count are unchanged — and it is also the routine that makes the evolved state: run it and the state is in hand, control and invert it and an estimation readout can call the whole simulation as a subroutine.

Records that are this object

Each of these is an instance of this state, filed in the catalogue with its own construction. The map does not know them individually — it knows the object, and these are what the object is.

Work that arrives here

Prepare an input state
Map $|0\ldots0⟩$ to a state whose amplitudes are proportional to a specified vector $b$ , to within $\varepsilon$ . The cost is set by which description of $b$ you hold, not by the algorithm that consumes it.
Minimise the objective over the parameters
Search the parameters of a fixed circuit family for the ones that minimise a chosen objective, given that every evaluation of that objective is a noisy estimate someone paid shots for. The output is a routine that prepares one particular state — the family collapsed to a member.

Work that starts here

Estimate an observable
Given the ability to prepare $|ψ⟩$ and a description of an observable $O$ , return a classical scalar within $\varepsilon$ of $⟨O⟩$ at confidence $1−δ$ . The state is never returned; only the number is.