State
Cost Hamiltonian, diagonal in the computational basis
An Ising or QUBO operator, diagonal in the computational basis. Its extremal computational-basis eigenstates are the optimal assignments a combinatorial optimisation problem is asking for — one or more of them, because two assignments tying on the objective is ordinary rather than a special case — and a general vector in that eigenspace is a superposition of them and not an assignment at all, which is why what comes back is measured in the computational basis rather than read off the operator. Nothing in this build produces it: the encoding slot that would turn a combinatorial-problem statement into this operator was scoped and then refused, so this is where the region starts, not a state anything hands off.
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
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
- Search a cost Hamiltonian for the assignment it minimises
A cost function over discrete assignments, rewritten as an operator diagonal in the computational basis, is searched for the assignment at or near its minimum — by alternating short unitaries at a fixed, chosen depth, or by interpolating continuously toward the operator's own ground state. Both routes read the same operator; what they promise about the assignment they hand back is where they differ.