PrepareSlaterDeterminant¶

class PrepareSlaterDeterminant(occupation, rotation_unitary, *, synthesis=None)¶

Bases: FermionicGate

Prepares a Slater determinant from an occupation and an orbital rotation.

This gate is the composition of an InitializeModes reference occupation followed by an OrbitalRotation: it declares that the modes it acts on start in the determinant defined by occupation and are then rotated by rotation_unitary. Because the initial occupation is known, decomposing this gate can use the rectangular givens_decomposition_slater() for a reduced-gate-count synthesis (see FermionicSlaterGivensDecomposition) rather than the full square decomposition an OrbitalRotation alone would require.

Following the OrbitalRotation convention \(a^\dagger_i \mapsto \sum_j U_{ji} a^\dagger_j\), rotating the occupied modes maps them onto the corresponding columns of rotation_unitary; those columns span the occupied space of the prepared Slater determinant.

Simulation semantics

Under simulation this gate is validate-then-rotate, not a state producer: given an incoming state vector it validates that the vector is confined to the subspace occupation defines (via InitializeModes) and then applies rotation_unitary (via OrbitalRotation). It therefore requires a real reference state vector, prepared externally (e.g. via ffsim.slater_determinant()). The producer behavior (emitting the gates that set the reference occupation) lives in the synthesis, not the simulation path.

Applying (rather than dropping) the rotation is what guarantees that merging an InitializeModes and an OrbitalRotation into this single gate leaves the simulated final state unchanged.

Decomposition semantics

Breaking this gate down in fermionic space is optional, and it is what the synthesis attribute governs. It defaults to FermionicSlaterGivensDecomposition. The two ways of breaking the gate down differ, and deliberately so:

the definition of the gate (what decompose() expands it into) is the InitializeModes of occupation followed by an OrbitalRotation. It is equivalent to the gate as an operator;
synthesis produces a circuit that prepares the same Slater determinant from the vacuum, up to a global phase. It is cheaper because it exploits the known reference, and equivalent to the gate as a state preparation only.

Note

No fermion-to-qubit plugin maps this gate directly. Break it down in fermionic space first, with the F2FSynthesis transpiler pass, so that the fermion-to-qubit stage only sees the gates it produces.

Caution

This is an early development prototype. Beware of changes to its interface without warning during the pre-release development of this package.