FermionicGaussianState#

class FermionicGaussianState(transformation_matrix, occupied_orbitals=None, qubit_mapper=None, *, validate=True, rtol=1e-05, atol=1e-08, **circuit_kwargs)[fuente]#

Bases: QuantumCircuit

A circuit that prepares a fermionic Gaussian state.

A fermionic Gaussian state is a state of the form

b_{1}^{†} \dots b_{N_{p}}^{†} | \overset{―}{vac} ⟩,

where

\begin{array}{r} (\begin{array}{c} b_{1}^{†} \\ ⋮ \\ b_{N}^{†} \end{array}) = W (\begin{array}{c} a_{1}^{†} \\ ⋮ \\ a_{N}^{†} \\ a_{1} \\ ⋮ \\ a_{N} \end{array}) . \end{array}

$a_{1}^{†}, \dots, a_{N}^{†}$ are the fermionic creation operators.
$W$ is an $N \times 2 N$ matrix such that $b_{1}^{†}, \dots, b_{N}^{†}$ also satisfy the fermionic anticommutation relations.
$| \overset{―}{vac} ⟩$ is the mutual 0-eigenvector of the operators ${b_{j}^{†} b_{j}}$ .

The matrix $W$ has the block form

(\begin{matrix} W_{1} & W_{2} \end{matrix}),

where $W_{1}$ and $W_{2}$ must satisfy

\begin{array}{r} W_{1} W_{1}^{†} + W_{2} W_{2}^{†} = I \\ W_{1} W_{2}^{T} + W_{2} W_{1}^{T} = 0. \end{array}

The matrix $W$ is commonly obtained by calling the diagonalizing_bogoliubov_transform() method of the QuadraticHamiltonian class. This matrix is used to create circuits that prepare eigenstates of the quadratic Hamiltonian.

Currently, only the Jordan-Wigner transformation is supported.

Reference: arXiv:1711.05395

Parámetros:

transformation_matrix (np.ndarray) – The matrix $W$ that specifies the coefficients of the new creation operators in terms of the original creation and annihilation operators. This matrix must satisfy special constraints, as detailed above.
occupied_orbitals (Sequence[int] | None) – The pseudo-particle orbitals to fill. These refer to the indices of the operators ${b_{j}^{†}}$ from the main body of the docstring of this function. The default behavior is to use the empty set of orbitals, which corresponds to a state with zero pseudo-particles.
qubit_mapper (QubitMapper | None) – The QubitMapper. The default behavior is to create one using the call JordanWignerMapper().
validate (bool) – Whether to validate the inputs.
rtol (float) – Relative numerical tolerance for input validation.
atol (float) – Absolute numerical tolerance for input validation.
circuit_kwargs – Keyword arguments to pass to the QuantumCircuit initializer.

Muestra:

ValueError – transformation_matrix must be a 2-dimensional array.
ValueError – transformation_matrix must have shape (n_orbitals, 2 * n_orbitals).
ValueError – transformation_matrix does not describe a valid transformation of fermionic ladder operators. A valid matrix has the block form $(W_{1} W_{2})$ where $W_{1} W_{1}^{†} + W_{2} W_{2}^{†} = I$ and $W_{1} W_{2}^{T} + W_{2} W_{1}^{T} = 0$ .
NotImplementedError – Currently, only the Jordan-Wigner Transform is supported. Please use the qiskit_nature.second_q.mappers.JordanWignerMapper.

Attributes

Methods