Simulating hydrogen molecule using qiskit-nature

You can design and simulate a molecular structure using qiskit-nature, which is an extension of Qiskit designed for quantum chemistry applications. Here’s how you can set up a quantum simulation of a molecule like (\text{H}_2) using Qiskit Nature:

Steps:

1. Define the molecule using its geometry.
2. Convert the molecular Hamiltonian into a qubit Hamiltonian.
3. Use a variational algorithm (VQE) to find the ground state energy.
4. Run it on a quantum backend.

Code to Simulate ( H_2 ) Molecule

from qiskit_nature.settings import settings
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.hamiltonians import ElectronicEnergy
from qiskit_nature.second_q.mappers import JordanWignerMapper
from qiskit.algorithms import VQE
from qiskit.primitives import Estimator
from qiskit.circuit.library import TwoLocal
from qiskit_ibm_runtime import QiskitRuntimeService, SamplerVQE, EstimatorVQE

# Ensure qubit reduction is disabled for full control
settings.use_symmetry_reduced_integrals = False

# Step 1: Define the molecular system (H2)
driver = PySCFDriver(atom="H 0 0 0; H 0 0 0.74", basis="sto3g")
problem = driver.run()

# Step 2: Convert to qubit Hamiltonian
mapper = JordanWignerMapper()
hamiltonian = problem.hamiltonian.second_q_op()
qubit_hamiltonian = mapper.map(hamiltonian)

# Step 3: Choose a variational ansatz and optimizer
ansatz = TwoLocal(rotation_blocks='ry', entanglement_blocks='cz', reps=2)
vqe = VQE(Estimator(), ansatz)

# Step 4: Run on quantum backend (Qiskit Runtime)
service = QiskitRuntimeService(channel="ibm_quantum")
backend = service.least_busy(simulator=False)  # Select fastest real device
estimator_vqe = EstimatorVQE(ansatz=ansatz, optimizer='SPSA')

# Compute ground state energy
result = estimator_vqe.compute_minimum_eigenvalue(qubit_hamiltonian)
print("Ground state energy:", result.eigenvalue.real)

Explanation:

1. Molecule Definition: Defines hydrogen ((\text{H}_2)) at 0.74Å bond length.
2. Hamiltonian Mapping: Uses the Jordan-Wigner transformation to convert it into a qubit Hamiltonian.
3. VQE Solver: Uses a parameterized quantum circuit to estimate the ground-state energy.
4. Quantum Execution: Runs on the fastest real quantum device using QiskitRuntimeService.