# openfermion.circuits.slater_determinant_preparation_circuit

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

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

.. math::

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


where

.. math::

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 :math:N_f orbitals filled.

slater_determinant_matrix The matrix :math: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 :math:(i, j, \theta, \varphi), indicating a Givens rotation of modes :math:i and :math:j by angles :math:\theta and :math:\varphi.