Unitary whose eigenphase is wanted

This is a kind of

Anything that asks for one of these will accept this, because it is narrower. The reverse does not hold.

• 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.

• 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.

• Circuit for e^{-iHt}

  Time evolution under a Hamiltonian, approximated to a stated error, with the query or gate count and the norm parameter the count is measured against. It is a circuit, not an answer — something still has to run it on a state and read the result.

• Abstract circuit

  Arbitrary rotation angles, arbitrary two-qubit gates, and any qubit able to talk to any other. No machine runs this. Everything between here and hardware is the business of closing that gap and counting what it costs.

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

• Estimate the eigenphase of a unitary

  Given a circuit whose controlled powers you can apply, and a routine preparing a state with non-negligible overlap on one of its eigenvectors, return that eigenvector's phase as a number with an error bar. The phase is read out of an ancilla, never out of the system register — the system is only ever the thing the controlled powers act on.

Also accepted where something broader is wanted

These ask for an object this one is a kind of. Narrowing composes in that direction and only that direction: handing on something broader than a process asks for would be a skipped conversion.

• 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.

• Compile a circuit to a specific device

  Turn a circuit written as arbitrary unitaries over abstract qubits into an executable instruction sequence for one machine's own gate set and connectivity graph. The result is functionally equivalent, or equivalent to within a stated approximation error.

• Satisfy the hardware connectivity constraint

  Place logical qubits on physical ones and schedule connectivity-repair operations — usually SWAPs — so that every two-qubit gate acts on a coupled pair. The problem combines subgraph isomorphism with token swapping.

• Approximate a continuous rotation in a discrete gate set

  Given a target single-qubit unitary — typically a z-rotation by an arbitrary angle — and a precision $\varepsilon$, produce a finite word over a fixed discrete gate set such as Clifford+T whose product is within $\varepsilon$ of the target in a stated metric. The cost is charged in non-Clifford gates.