SlaterDeterminant

class SlaterDeterminant(transformation_matrix, qubit_mapper=None, *, validate=True, rtol=1e-05, atol=1e-08, **circuit_kwargs)

Bases: QuantumCircuit

A circuit that prepares a Slater determinant.

A Slater determinant is a state of the form

$$b_1^{†}\cdots b_{N_f}^{†}|\text{vac}⟩,$$

where

$$b_j^{†}=\sum _{k=1}^N{Q}_{jk}{a}_k^{†}.$$

• $Q$ is an $N_f\times N$ matrix with orthonormal rows.

• $a_1^{†},\dots ,a_N^{†}$ are the fermionic creation operators.

• $|\text{vac}⟩$ is the vacuum state. (mutual 0-eigenvector of the fermionic number operators $\{a_j^{†}{a}_j\}$)

The matrix $Q$ can be obtained by calling the diagonalizing_bogoliubov_transform() method of the QuadraticHamiltonian class when the quadratic Hamiltonian conserves particle number. 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 $Q$ that specifies the coefficients of the new creation operators in terms of the original creation operators. The rows of the matrix must be orthonormal.

• 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.

• NotImplementedError – Currently, only the Jordan-Wigner Transform is supported. Please use the qiskit_nature.second_q.mappers.JordanWignerMapper.

Attributes

Methods