State
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.
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
- Linear system Ax = b
One matrix and one right-hand side, with the whole time history folded into them. It has a condition number, and that number is what the cost of solving it will be measured against. Every solver in the literature is handed it as an access model for the matrix plus a routine preparing the right-hand side, which is why it counts as a matrix you can query.
- Block-encoding
A unitary whose top-left block is the matrix you care about, divided by a subnormalisation α. Because the unitary has norm one, α is not a free parameter — it bounds the matrix, and it multiplies straight into every cost downstream.
- 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.
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
- 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.