BogoliubovTransform#

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

Bases: QuantumCircuit

A circuit that performs a Bogoliubov transform.

A Bogoliubov transform effects a unitary basis change that maps the fermionic ladder operators to a new set of ladder operators that also satisfy the fermionic anticommutation relations. That is, it effects a unitary $U$ such that

U a_{j}^{†} U^{†} = b_{j}^{†}, j = 1, \dots, N

where the ${a_{j}}$ are the original fermionic creation operators and the ${b_{j}}$ are the new fermionic creation operators. The new creation operators are linear combinations of the original ladder operators, and the coefficients of the linear combinations are specified by a matrix $W$ which determines the unitary $U$ . The matrix $W$ is either $N \times N$ or $N \times 2 N$ .

If $W$ is $N \times N$ , then the linear combinations involve only the original creation operators:

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

If $W$ is $N \times 2 N$ , then the linear combinations involve both the original creation and annihilation operators:

\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}

The matrix $W$ is commonly obtained by calling the diagonalizing_bogoliubov_transform() method of the QuadraticHamiltonian class.

Currently, only the Jordan-Wigner Transformation is supported.

Referencias

Parámetros:

transformation_matrix (np.ndarray) – The matrix $W$ that specifies the coefficients of the new creation operators in terms of the original creation operators. Should be either $N \times N$ or $N \times 2 N$ .
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 orthonormal rows.
ValueError – transformation_matrix does not describe a valid transformation of fermionic ladder operators. If the transformation matrix is $N \times N$ , then it should be unitary. If the transformation matrix is $N \times 2 N$ , then it should have 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