qubit-efficient-mapping

Introduction

A qubit-efficient tool to map second-quantized fermionic operators into qubit(Pauli) operators for further variational quantum algorithms.

Dependencies

• Qiskit: 0.23.5

Tutorial

First, construct a QMolecule object with PySCFDriver, e.g. a hydrogen molecule with interatomic distance dist(A) in STO-3G basis set.

from qiskit.chemistry.drivers import PySCFDriver, UnitsType
dist = .7
driver = PySCFDriver(atom="H .0 .0 .0; H .0 .0 " + str(dist), unit=UnitsType.ANGSTROM, 
                         charge=0, spin=0, basis='sto-3g')
molecule = driver.run()
num_electrons = molecule.num_alpha + molecule.num_beta

Then, a FermionicOperator object can be constructed using one- and two-body intergrals in molecule.

ferOp = FermionicOperator(h1=molecule.one_body_integrals, h2=molecule.two_body_integrals)

Now, groupedFermionicOperator helps us tranform the fermionic operators(ferOp) into qubit operators(qubitOp). The to_paulis method returns the qubit operator based on our mapping method.

from groupedFermionicOperator import groupedFermionicOperator

g = groupedFermionicOperator(ferOp, num_electrons)
qubitOp = g.to_paulis()

To verify the result, one may calculate the lowest eigenvalue of the qubit operator, and compare the result with that from built-in Jordan-Wigner transform etc.

from qiskit.aqua.algorithms import NumPyEigensolver
result_exact = NumPyEigensolver(qubitOp).run()
energy_exact = (np.real(result_exact.eigenvalues))[0]
print(energy_exact)

qubitOpJW = ferOp.mapping(map_type='jordan_wigner', threshold=1e-6)
result_exactJW = NumPyEigensolver(qubitOpJW).run()
energy_exactJW = (np.real(result_exactJW.eigenvalues))[0]
print(energy_exactJW)