pychemiq.Transform#

Module Contents#

The mapping submodule is responsible for mapping fermionic operators to Pauli operators. When using a UCC ansatz to construct a parameterized quantum circuit for preparing the trial wavefunction, we need to specify the mapping type of the unitary coupled-cluster operator. This is done via pychemiq.Transform.mapping.MappingType. Importantly, the mapping type used here must be consistent with the mapping method applied to the Hamiltonian — that is, the same mapping scheme must be the same both in mapping fermion operators and ansatz mapping in the calculation.

Classes#

class pychemiq.Transform.mapping.MappingType#

The MappingType enumeration class has four different values, namely:

Bravyi_Kitaev#
Jordan_Wigner#
Parity#
SegmentParity#

Interface Example:

from pychemiq import ChemiQ,QMachineType
from pychemiq.Transform.Mapping import MappingType
from pychemiq.Circuit.Ansatz import UCC

chemiq = ChemiQ()
machine_type = QMachineType.CPU_SINGLE_THREAD
# Using JW mapping method
mapping_type = MappingType.Jordan_Wigner
# Using BK mapping method
# mapping_type = MappingType.Bravyi_Kitaev
# Using Parity mapping method
# mapping_type = MappingType.Parity
# Using SegmentParity mapping method
# mapping_type = MappingType.SegmentParity
chemiq.prepare_vqe(machine_type,mapping_type,2,1,4)
ansatz = UCC("UCCSD",2,mapping_type,chemiq=chemiq)

Functions#

pychemiq.Transform.mapping.jordan_wigner(fermion)#

Map the input fermionic operator into a Pauli operator through the Jordan Wigner transformation.

Parameters:

fermion (FermionOperator) – Enter the fermionic operator to be mapped.

Returns:

The mapped Pauli operator. Pauli operator class.

pychemiq.Transform.mapping.bravyi_kitaev(fermion)#

Map the input fermionic operator into a Pauli operator through the Bravyi Kitaev transformation.

Parameters:

fermion (FermionOperator) – Enter the fermionic operator to be mapped.

Returns:

The mapped Pauli operator. Pauli operator class.

pychemiq.Transform.mapping.parity(fermion)#

Map the input fermionic operator into a Pauli operator through Parity transformation.

Parameters:

fermion (FermionOperator) – Enter the fermionic operator to be mapped.

Returns:

The mapped Pauli operator. Pauli operator class.

pychemiq.Transform.mapping.segment_parity(fermion)#

Map the input fermionic operator through segment_party transformation maps to the Pauli operator.

Parameters:

fermion (FermionOperator) – Enter the fermionic operator to be mapped.

Returns:

The mapped Pauli operator. Pauli operator class.

Interface example:

In the following example, we use the above four mapping methods to map the Hamiltonian of the hydrogen molecule after second-quantization from the fermionic operator to the form of the Pauli operator. Firstly, initialize the electronic structure parameters of the molecule to obtain the Hamiltonian in fermionic form.

from pychemiq import Molecules

multiplicity = 1
charge = 0
basis =  "sto-3g"
geom = "H 0 0 0,H 0 0 0.74"

mol = Molecules(
geometry = geom,
basis    = basis,
multiplicity = multiplicity,
charge = charge)
fermion_H2 = mol.get_molecular_hamiltonian()

Next thing is to obtain the Hamiltonian of hydrogen molecules in Pauli form through JW transformation and print the results.

from pychemiq.Transform.Mapping import jordan_wigner
pauli_H2 = jordan_wigner(fermion_H2)
print(pauli_H2)

{
"" : -0.097066,
"X0 X1 Y2 Y3" : -0.045303,
"X0 Y1 Y2 X3" : 0.045303,
"Y0 X1 X2 Y3" : 0.045303,
"Y0 Y1 X2 X3" : -0.045303,
"Z0" : 0.171413,
"Z0 Z1" : 0.168689,
"Z0 Z2" : 0.120625,
"Z0 Z3" : 0.165928,
"Z1" : 0.171413,
"Z1 Z2" : 0.165928,
"Z1 Z3" : 0.120625,
"Z2" : -0.223432,
"Z2 Z3" : 0.174413,
"Z3" : -0.223432
}

Or to obtain the Hamiltonian of hydrogen molecules in Pauli form through BK transformation and print the results.

from pychemiq.Transform.Mapping import bravyi_kitaev
pauli_H2 = bravyi_kitaev(fermion_H2)
print(pauli_H2)

{
"" : -0.097066,
"X0 Z1 X2" : 0.045303,
"X0 Z1 X2 Z3" : 0.045303,
"Y0 Z1 Y2" : 0.045303,
"Y0 Z1 Y2 Z3" : 0.045303,
"Z0" : 0.171413,
"Z0 Z1" : 0.171413,
"Z0 Z1 Z2" : 0.165928,
"Z0 Z1 Z2 Z3" : 0.165928,
"Z0 Z2" : 0.120625,
"Z0 Z2 Z3" : 0.120625,
"Z1" : 0.168689,
"Z1 Z2 Z3" : -0.223432,
"Z1 Z3" : 0.174413,
"Z2" : -0.223432
}

Or to obtain the Hamiltonian of hydrogen molecules in Pauli form through Parity transformation and print the results.

from pychemiq.Transform.Mapping import parity
pauli_H2 = parity(fermion_H2)
print(pauli_H2)

{
"" : -0.097066,
"X0 Z1 X2" : 0.045303,
"X0 Z1 X2 Z3" : 0.045303,
"Y0 Y2" : 0.045303,
"Y0 Y2 Z3" : 0.045303,
"Z0" : 0.171413,
"Z0 Z1" : 0.171413,
"Z0 Z1 Z2" : 0.120625,
"Z0 Z1 Z2 Z3" : 0.120625,
"Z0 Z2" : 0.165928,
"Z0 Z2 Z3" : 0.165928,
"Z1" : 0.168689,
"Z1 Z2" : -0.223432,
"Z1 Z3" : 0.174413,
"Z2 Z3" : -0.223432
}

Or to obtain the Hamiltonian of hydrogen molecules in Pauli form through SP transformation and print the results.

from pychemiq.Transform.Mapping import segment_parity
pauli_H2 = segment_parity(fermion_H2)
print(pauli_H2)

{
"" : -0.097066,
"X0 Z1 X2" : 0.045303,
"X0 Z1 X2 Z3" : 0.045303,
"Y0 Z1 Y2" : 0.045303,
"Y0 Z1 Y2 Z3" : 0.045303,
"Z0" : 0.171413,
"Z0 Z1" : 0.171413,
"Z0 Z1 Z2" : 0.165928,
"Z0 Z1 Z2 Z3" : 0.165928,
"Z0 Z2" : 0.120625,
"Z0 Z2 Z3" : 0.120625,
"Z1" : 0.168689,
"Z1 Z2 Z3" : -0.223432,
"Z1 Z3" : 0.174413,
"Z2" : -0.223432
}