BASF: Quantum Chemistry Simulation for Catalyst Design

The Problem

Nitrogen fixation, converting atmospheric nitrogen into ammonia, is one of the most important chemical reactions on Earth. The Haber-Bosch industrial process produces ammonia for fertilizers that feed roughly half the global population, but it operates at high temperatures and pressures and consumes about 1-2% of global energy.

Nature does the same reaction at room temperature and pressure using an enzyme called nitrogenase, which contains a complex metal cluster called FeMo-co (iron-molybdenum cofactor). If chemists could design a synthetic catalyst that mimics FeMo-co, it could revolutionize fertilizer production.

The obstacle is computational. FeMo-co involves 54 strongly correlated electrons across multiple metal atoms. Classical quantum chemistry methods (DFT, CCSD(T)) either cannot handle this accurately or scale exponentially in cost. This is precisely the class of problem where quantum computers are expected to help.

VQE for Molecular Simulation

The Variational Quantum Eigensolver (VQE) uses a quantum computer to prepare trial molecular states and measure their energy, then uses a classical optimizer to minimize that energy. The lowest energy state is the molecular ground state, which determines chemical behavior.

Internally, Quantum Phase Estimation (QPE), which relies on the Quantum Fourier Transform (QFT), is the fault-tolerant alternative to VQE that would be used for accurate large-molecule simulation.

BASF’s proof-of-concept work used VQE on IBM hardware to simulate H2 and LiH:

from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import JordanWignerMapper
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_algorithms import VQE
from qiskit_algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD

# Set up H2 molecule at equilibrium bond length
driver = PySCFDriver(atom="H 0 0 0; H 0 0 0.735", basis="sto3g")
problem = driver.run()

# Map fermionic Hamiltonian to qubit operators
mapper = JordanWignerMapper()

# Build ansatz: unitary coupled cluster singles and doubles
num_particles = problem.num_particles
num_spatial_orbitals = problem.num_spatial_orbitals

ansatz = UCCSD(
    num_spatial_orbitals=num_spatial_orbitals,
    num_particles=num_particles,
    mapper=mapper,
    initial_state=HartreeFock(
        num_spatial_orbitals=num_spatial_orbitals,
        num_particles=num_particles,
        mapper=mapper,
    ),
)

# Run VQE
estimator = Estimator()
optimizer = SLSQP(maxiter=500)
vqe = VQE(estimator=estimator, ansatz=ansatz, optimizer=optimizer)

solver = GroundStateEigensolver(mapper, vqe)
result = solver.solve(problem)

print(f"Ground state energy: {result.total_energies[0]:.6f} Hartree")
# Expected: ~-1.1373 Hartree for H2 at equilibrium

Why QFT Matters Here

VQE is a near-term heuristic: it works on noisy hardware but cannot guarantee accuracy for large systems. The fault-tolerant alternative is Quantum Phase Estimation (QPE).

QPE works by encoding the molecular energy as a phase of a quantum state, then using the QFT to extract that phase as a bitstring. The QFT maps between the “time” and “frequency” domains of a quantum signal, exactly as a classical Fourier transform does, but operating on quantum amplitudes.

For FeMo-co, QPE-based simulation would require:

• Around 4000 logical qubits (error-corrected)
• Millions of physical qubits given current error rates
• Circuit depths requiring coherence times far beyond current hardware

Results

BASF’s VQE experiments on IBM Quantum hardware confirmed the molecular ground state energies for H2 and LiH to within chemical accuracy on simulators, with noisy hardware results requiring error mitigation. The computed energies matched classical results from CCSD.

For FeMo-co, the team published detailed resource estimates. The conclusion is unambiguous: the quantum resources needed for industrially useful molecular simulation do not exist yet and will not for at least a decade.

The Value of the Work Now

Running these experiments today, even on toy molecules, is essential groundwork:

1. Algorithm development: Discovering which ansatz circuits best capture electron correlation
2. Error mitigation: Learning which classical corrections produce reliable results on noisy hardware
3. Resource estimation: Quantifying exactly how much hardware improvement is needed
4. Toolchain maturity: Building the software stack that will run on future hardware

BASF’s investment is a long-term positioning move. The company that has already developed the workflows and domain expertise will be best placed to exploit fault-tolerant hardware when it arrives.

Framework

BASF used Qiskit and Qiskit Nature for molecular Hamiltonian construction and VQE. IBM Quantum hardware provided the execution environment. Academic collaborators contributed classical quantum chemistry benchmarks.

Learn more: Qiskit Reference