FermionicOperator

class FermionicOperator(h1, h2=None, ph_trans_shift=None)[source]

A set of functions to map fermionic Hamiltonians to qubit Hamiltonians.

References:

  • E. Wigner and P. Jordan., Über das Paulische Äquivalenzverbot, Z. Phys., 47:631 (1928).

  • S. Bravyi and A. Kitaev. Fermionic quantum computation, Ann. of Phys., 298(1):210–226 (2002).

  • A. Tranter, S. Sofia, J. Seeley, M. Kaicher, J. McClean, R. Babbush, P. Coveney, F. Mintert, F. Wilhelm, and P. Love. The Bravyi–Kitaev transformation: Properties and applications. Int. Journal of Quantum Chemistry, 115(19):1431–1441 (2015).

  • S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, arXiv e-print arXiv:1701.08213 (2017).

  • K. Setia, J. D. Whitfield, arXiv:1712.00446 (2017)

This class requires the integrals stored in the ‘chemist’ notation

h2(i,j,k,l) –> adag_i adag_k a_l a_j

and the integral values are used for the coefficients of the second-quantized Hamiltonian that is built. The integrals input here should be in block spin format and also have indexes reordered as follows ‘ijkl->ljik’

There is another popular notation, the ‘physicist’ notation

h2(i,j,k,l) –> adag_i adag_j a_k a_l

If you are using the ‘physicist’ notation, you need to convert it to the ‘chemist’ notation. E.g. h2=numpy.einsum(‘ikmj->ijkm’, h2)

The QMolecule class has one_body_integrals and two_body_integrals properties that can be directly supplied to the h1 and h2 parameters here respectively.

Parameters

  • h1 (numpy.ndarray) – second-quantized fermionic one-body operator, a 2-D (NxN) tensor

  • h2 (numpy.ndarray) – second-quantized fermionic two-body operator, a 4-D (NxNxNxN) tensor

  • ph_trans_shift (float) – energy shift caused by particle hole transformation

Attributes

FermionicOperator.h1

Getter of one body integral tensor.

FermionicOperator.h2

Getter of two body integral tensor.

FermionicOperator.modes

Getter of modes.

Methods

FermionicOperator.fermion_mode_elimination(…)

Eliminate modes.

FermionicOperator.fermion_mode_freezing(…)

Freezing modes and extracting its energy.

FermionicOperator.mapping(map_type[, threshold])

Map fermionic operator to qubit operator.

FermionicOperator.particle_hole_transformation(…)

The ‘standard’ second quantized Hamiltonian can be transformed in the particle-hole (p/h) picture, which makes the expansion of the trail wavefunction from the HF reference state more natural.

FermionicOperator.total_angular_momentum()

Total angular momentum.

FermionicOperator.total_magnetization()

A data_preprocess_helper fermionic operator which can be used to evaluate the magnetization of the given eigenstate.

FermionicOperator.total_particle_number()

A data_preprocess_helper fermionic operator which can be used to evaluate the number of particle of the given eigenstate.

FermionicOperator.transform(unitary_matrix)

Transform the one and two body term based on unitary_matrix.