qiskit.chemistry.FermionicOperator
class FermionicOperator(h1, h2=None, ph_trans_shift=None)
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__
__init__(h1, h2=None, ph_trans_shift=None)
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
fermion_mode_elimination
fermion_mode_elimination(fermion_mode_array)
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
fermion_mode_freezing
fermion_mode_freezing(fermion_mode_array)
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)
h1
Getter of one body integral tensor.
h2
Getter of two body integral tensor.
mapping
mapping(map_type, threshold=1e-08)
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
Raises
QiskitChemistryError – if the map_type can not be recognized.
modes
Getter of modes.
particle_hole_transformation
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. 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
total_angular_momentum()
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
total_magnetization
total_magnetization()
A data_preprocess_helper fermionic operator which can be used to evaluate the magnetization of the given eigenstate.
Returns
Fermionic Hamiltonian
Return type
total_particle_number
total_particle_number()
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
transform
transform(unitary_matrix)
Transform the one and two body term based on unitary_matrix.