State
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.
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.
- 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
- Hermitian generator
A linear generator that happens to be Hermitian, so the evolution it drives is unitary and a simulator can run it as it stands. This is why some lifts reach an answer without ever assembling a linear system.
- 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.
- 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.
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.
- Fermi-Hubbard dimer operator (Jordan-Wigner encoded)
- H₂ molecular qubit Hamiltonian (STO-3G, 2-qubit tapered)
- Heisenberg XXZ spin-chain operator
- Classical Ising Hamiltonian operator
- Bose–Hubbard Hamiltonian
- Electronic-structure Hamiltonian
- Fermi–Hubbard Hamiltonian
- Heisenberg Hamiltonian
- Ising cost Hamiltonian
- Kitaev-chain Hamiltonian
- MaxCut cost operator
- Transverse-field Ising Hamiltonian
- Weighted Pauli-sum Hamiltonian
- XY spin Hamiltonian
- XYZ spin Hamiltonian
- Transverse-field Ising model operator
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
- Simulate Hamiltonian evolution
Implement to error given some access model for . It is an application in its own right and also the engine inside phase estimation and several linear-system solvers.
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 inside a larger unitary so that sits in 's top-left block, giving every routine above it one uniform way to touch the matrix. The subnormalization and the ancilla count are outputs of this layer, not free parameters.