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MethodLayer 2

The mapping paper that names VQE as the reason to frame a ground-state question

Realises `ground-state-framing` on one citation: a ternary-tree fermion-to-qubit mapping paper whose own first section states, in passing, that an efficient encoding matters because a caller downstream -- naming VQE by name -- is going to ask for a ground state. The mapping itself is not drawn here; only the sentence that motivates it is.

Takes

A Hermitian operator reachable as a sum of terms, as sparse-access oracles or as a block-encoding -- exactly what hamiltonian-access already promises -- plus the one thing no prior process can hand over: the caller's own declaration that the quantity being asked for is that operator's lowest eigenvalue rather than, say, its state at a later time.

Returns

The identical operator, now typed as a ground-state-problem. Nothing about the Hamiltonian is transformed; the whole content of this step is the declaration attached to it.

Same contract as the slot it fills.

This one, drawn

The mapping paper that names VQE as the reason to frame a ground-state questionThe mapping paper that names VQE as the reason to frame a ground-state questionThe mapping paper that names VQE as the reason to frame a ground-state question — click the name to read about itCited for the VQE framing claimHamiltonian you can query — you start hereHamiltonian whose ground state is wanted — you finish here

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From Hamiltonian you can query to Hamiltonian whose ground state is wanted

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What it fills

  • Frame an operator as a ground-state question

    Given a Hamiltonian reachable as hamiltonian-access, plus the caller's own declaration that the quantity wanted is its lowest eigenvalue rather than its time evolution, return the same operator typed as a ground-state-problem -- the entry `ground-state-energy`, and every method realising it, is written against.

When it applies

Jiang, Kalev, Mruczkiewicz and Neven open by motivating why an efficient fermion-to-qubit mapping matters at all, and the sentence names the caller's declaration directly: "Having an efficient, simple, fermion-to-qubit mapping is a key ingredient in any quantum simulation protocol, e.g., the variational quantum eigensolver (VQE) [12, 13]." The paper's own construction -- a ternary-tree encoding proven optimal on average Pauli weight -- is a different, competing-methods question that W32 scoped and refused separately (plans/atlas-revamp/W32-fermion-to-qubit-mapping.md §3); nothing about that refusal touches this sentence, which is about what VQE consumes rather than about how an operator is encoded.

Requires

Every step this method names moves its route along, so there is nothing it needs alongside them.

Example

given  H, a Hamiltonian reachable as hamiltonian-access -- a sum of terms,
       sparse-access oracles, or a block-encoding                    (state-vocabulary.ts)
       the caller's own declaration that the quantity wanted is H's lowest
       eigenvalue, rather than its state under time evolution -- nothing on
       this map computes that declaration; it is what the caller brought

# Jiang, Kalev, Mruczkiewicz and Neven's own contribution is a ternary-tree
#   fermion-to-qubit encoding, not this step. Their introduction states, in
#   passing, the reason a caller downstream would run this step at all:
#   "fermion-to-qubit mapping is a key ingredient in any quantum simulation
#   protocol, e.g., the variational quantum eigensolver (VQE)"      (Sec. 1)

return  H, now typed ground-state-problem
# no term of H is read, written or transformed -- the whole content of this
#   step is the declaration attached to it

Cost, as the source states it

Jiang, Kalev, Mruczkiewicz and Neven price their ternary-tree fermion-to-qubit mapping (Theorem 1: average Pauli weight at least log base 3 of 2n, saturated constructively) -- a different, competing-methods question W32 scoped and refused separately. The sentence this method realises is a one-line motivation in their introduction, naming VQE as an example consumer of an efficient encoding; the paper attaches no resource count to that sentence itself, and there is none to report.

Implementations

Nobody has written one up yet. That is a gap in this record, not a statement that the method has never been run — the paper register already records, per paper, which sources report numerics or a hardware run.

What it needs

Nobody has taken this apart yet. That is a gap in this graph, not a claim that the method has no parts.

Other ways to fill the same slot

Nothing else in this graph fills this slot.

In the Atlas

No record in the Atlas covers this yet. The catalogue is circuits and primitives; this part of the literature is not in it.

Sources

1