# openfermion.circuits.slater_determinant_preparation_circuit

Obtain the description of a circuit which prepares a Slater determinant.

The input is an $$N_f \times N$$ matrix $$Q$$ with orthonormal rows. Such a matrix describes the Slater determinant

$b^\dagger_1 \cdots b^\dagger_{N_f} \lvert \text{vac} \rangle,$

where

$b^\dagger_j = \sum_{k = 1}^N Q_{jk} a^\dagger_k.$

The output is the description of a circuit which prepares this Slater determinant, up to a global phase. The starting state which the circuit should be applied to is a Slater determinant (in the computational basis) with the first $$N_f$$ orbitals filled.

slater_determinant_matrix The matrix $$Q$$ which describes the Slater determinant to be prepared.

circuit_description A list of operations describing the circuit. Each operation is a tuple of elementary operations that can be performed in parallel. Each elementary operation is a tuple of the form $$(i, j, \theta, \varphi)$$, indicating a Givens rotation of modes $$i$$ and $$j$$ by angles $$\theta$$ and $$\varphi$$.

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{"lastModified": "Last updated 2024-04-26 UTC."}