qiskit.chemistry.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

__init__(h1, h2=None, ph_trans_shift=None)[source]¶

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

Methods

`__init__`(h1[, h2, ph_trans_shift])	This class requires the integrals stored in the ‘chemist’ notation
`fermion_mode_elimination`(fermion_mode_array)	Eliminate modes.
`fermion_mode_freezing`(fermion_mode_array)	Freezing modes and extracting its energy.
`mapping`(map_type[, threshold])	Map fermionic operator to qubit operator.
`particle_hole_transformation`(num_particles)	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.
`total_angular_momentum`()	Total angular momentum.
`total_magnetization`()	A data_preprocess_helper fermionic operator which can be used to evaluate the magnetization of the given eigenstate.
`total_particle_number`()	A data_preprocess_helper fermionic operator which can be used to evaluate the number of particle of the given eigenstate.
`transform`(unitary_matrix)	Transform the one and two body term based on unitary_matrix.

Attributes

`h1`	Getter of one body integral tensor.
`h2`	Getter of two body integral tensor.
`modes`	Getter of modes.

fermion_mode_elimination(fermion_mode_array)[source]¶

Eliminate modes.

Generate a new fermionic operator with the modes in fermion_mode_array deleted

Parameters: fermion_mode_array (list) – orbital index for elimination
Returns: Fermionic Hamiltonian
Return type: FermionicOperator

fermion_mode_freezing(fermion_mode_array)[source]¶

Freezing modes and extracting its energy.

Generate a fermionic operator with the modes in fermion_mode_array deleted and provide the shifted energy after freezing.

Parameters: fermion_mode_array (list) – orbital index for freezing
Returns: Fermionic Hamiltonian and energy of frozen modes
Return type: tuple(FermionicOperator, float)

property h1¶: Getter of one body integral tensor.

property h2¶: Getter of two body integral tensor.

mapping(map_type, threshold=1e-08)[source]¶

Map fermionic operator to qubit operator.

Using multiprocess to speedup the mapping, the improvement can be observed when h2 is a non-sparse matrix.

Parameters

map_type (str) – case-insensitive mapping type. “jordan_wigner”, “parity”, “bravyi_kitaev”, “bksf”
threshold (float) – threshold for Pauli simplification

Returns

create an Operator object in Paulis form.

Return type

WeightedPauliOperator

Raises

QiskitChemistryError – if the map_type can not be recognized.

property modes¶: Getter of modes.

particle_hole_transformation(num_particles)[source]¶

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. In fact, for both trail wavefunctions implemented in q-lib (‘heuristic’ hardware efficient and UCCSD) the p/h Hamiltonian improves the speed of convergence of the VQE algorithm for the calculation of the electronic ground state properties. For more information on the p/h formalism see: P. Barkoutsos, arXiv:1805.04340(https://arxiv.org/abs/1805.04340).

Parameters: num_particles (list, int) – number of particles, if it is a list, the first number is alpha and the second number is beta.
Returns: new_fer_op, energy_shift
Return type: tuple

total_angular_momentum()[source]¶

Total angular momentum.

A data_preprocess_helper fermionic operator which can be used to evaluate the total angular momentum of the given eigenstate.

Returns: Fermionic Hamiltonian
Return type: FermionicOperator

total_magnetization()[source]¶

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

Returns: Fermionic Hamiltonian
Return type: FermionicOperator

total_particle_number()[source]¶

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

Returns: Fermionic Hamiltonian
Return type: FermionicOperator

transform(unitary_matrix)[source]¶: Transform the one and two body term based on unitary_matrix.