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

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


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

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 $\varphi$.