qat.fermion.hamiltonians.ElectronicStructureHamiltonian

class qat.fermion.hamiltonians.ElectronicStructureHamiltonian(hpq: ndarray, hpqrs: ndarray = None, constant_coeff: float = 0.0)

A container for the electronic-structure Hamiltonian, defined as

\[H = \sum_{pq} h_{pq}a_p^\dagger a_q + \frac{1}{2} \sum_{pqrs} h_{pqrs}a_p^\dagger a_q^\dagger a_r a_s + c \mathbb{I}\]
Parameters:

  • hpq (np.ndarray) – Array \(h_{pq}\). Must be 2D.

  • hpqrs (np.ndarray) – Array \(h_{pqrs}\). Must be 4D.

  • constant_coeff (float) – Constant coefficient \(c.\)

hpq

Array \(h_{pq}\).

Type:

np.ndarray

hpqrs

Array \(h_{pqrs}\).

Type:

np.ndarray

constant_coeff

Constant coefficient \(c\).

Type:

float

Example

import numpy as np
from qat.fermion import ElectronicStructureHamiltonian

h_pq = 0.2 * np.array([[0, 1], [1, 0]])
h_pqrs = np.zeros((2, 2, 2, 2))
h_pqrs[0, 1, 1, 0] = 0.7
h_pqrs[1, 0, 0, 1] = 0.7
hamiltonian = ElectronicStructureHamiltonian(h_pq, h_pqrs, -6)

print(f"H = {hamiltonian}")
eigvals = np.linalg.eigvalsh(hamiltonian.get_matrix())

print(f"eigenvalues = {eigvals}")

H = -6 * I^2 +
0.2 * (Cc|[0, 1]) +
0.2 * (Cc|[1, 0]) +
-0.7 * (CCcc|[0, 1, 0, 1])
eigenvalues = [-6.2 -6.  -5.8 -5.3]
copy()

Deepcopy the current class.

Returns:

Copy of the ElectronicStructureHamiltonian.

Return type:

ElectronicStructureHamiltonian

dag() → ElectronicStructureHamiltonian

Compute the conjugate transpose of the Hamiltonian.

Returns:

Conjugate transpose of the Hamiltonian.

Return type:

ElectronicStructureHamiltonian

get_matrix(sparse: bool = False) → ndarray

This function returns the matrix corresponding to \(H\) in the computational basis.

Parameters:

  • sparse (Optional[bool]) – Whether to return in sparse representation.

  • False. (Defaults to)

Returns:

The matrix of the FermionHamiltonian.

Return type:

numpy.ndarray

Warning

This method should not be used if the Hamiltonian is too large.

to_fermion() → FermionHamiltonian

Convert current ElectronicStructureHamiltonian to a FermionHamiltonian.

Returns:

Fermionic Hamiltonian.

Return type:

FermionHamiltonian

to_spin(method: str | None = 'jordan-wigner')

Maps the fermionic Hamiltonian to a spin Hamiltonian.

Parameters:

method (str, optional) –

Method to use for the transformation to a spin representation. Available methods are :

  • ”jordan-wigner” : Jordan-Wigner transform (default),

  • ”bravyi-kitaev” : Bravyi-Kitaev transform,

  • ”parity” : Parity transform.

Returns:

Hamiltonian in spin representation.

Return type:

SpinHamiltonian