State

Hamiltonian surrogate, with the map back

A Hermitian generator manufactured from one that was not — on a space at least as large as the one you were in — whose unitary evolution carries the non-unitary dynamics you started with, together with the map that reads the original solution back out. The map is part of the object rather than an afterthought: it is where the norm the true dynamics lost gets paid back, and it is the half that costs.

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 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

Recast a non-Hermitian generator as Hamiltonian evolution
Given a generator $A(t)$ whose evolution is not unitary, produce a Hermitian generator — or a quadrature-indexed family of them — on a space at least as large, whose unitary evolution reproduces the original dynamics, together with the map that recovers the original solution. Both halves are required: a construction that reaches a Hamiltonian and cannot get back is not a route.

Work that starts here

No process asks for this by name. The ones below ask for something broader, and this is a kind of it — so they take it as it stands.

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.