State

Hamiltonian whose excited state is wanted

A Hamiltonian you can query, plus a declaration of which state above the lowest one is being asked for — the k-th, the lowest in a chosen symmetry sector, or the one nearest a target energy. That target is part of the problem, not a setting: a method that finds the ground state has not answered this question, and most methods here need the ground state before they can start.

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

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

Hamiltonian whose eigenvalues are wanted
A Hamiltonian you can query, plus the declaration that what is being asked for is a piece of its spectrum rather than an evolution under it. Which piece — the bottom of it, or a state above the bottom — is the next distinction down, and the two are separate states because the methods that answer them do not substitute for one another.
Hamiltonian you can query
A Hermitian operator reachable as a sum of terms you can exponentiate one at a time, as sparse-access oracles, or as a block-encoding — plus the norm parameter the simulation cost will be quoted against.
Matrix you can query
Some way of asking about a matrix without writing it down — sparse row and column oracles, a Pauli or LCU decomposition, a purification, or an explicit arithmetic rule. Which one you have decides which routes are open.

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 an excited-state energy
Given a Hamiltonian you can query and a statement of which state above the lowest one is wanted, return an estimate of that state's energy — or of its distance from the ground state, which is the quantity an experiment usually measures. Whether the answer comes back as an absolute energy or as an excitation energy is a property of the method, and the two are not interchangeable.

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.

Block-encode a matrix
Wrap an operator $A$ inside a larger unitary $U$ so that $A/α$ sits in $U$ 's top-left block, giving every routine above it one uniform way to touch the matrix. The subnormalization $α$ and the ancilla count are outputs of this layer, not free parameters.
Simulate Hamiltonian evolution
Implement $e^{-iHt}$ to error $\varepsilon$ given some access model for $H$ . It is an application in its own right and also the engine inside phase estimation and several linear-system solvers.
Choose a parameterised trial state
Fix the gate structure of a circuit family and leave its rotation angles open. What comes back is not a circuit but the set of states the later optimisation is allowed to search — which is why this is a slot of its own and not a paragraph in one method's write-up.