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 \(\varphi\).