Pfizer: Quantum Chemistry Simulation for Drug-Protein Binding

The Problem

When a drug candidate molecule binds to a protein target, the strength of that binding is captured by the binding free energy. This single thermodynamic number largely determines whether a drug will work. Computing it accurately requires modeling the electronic structure of the active site, a region that in realistic targets involves 50 or more atoms.

Classical quantum chemistry methods like Density Functional Theory (DFT) handle small systems well but lose accuracy as systems grow. The gold-standard classical method, CCSD(T), is accurate but scales as O(N^7) in system size. For a 50-atom active site, exact classical simulation is out of reach.

Pfizer’s quantum team, in collaboration with IBM, explored whether the Variational Quantum Eigensolver could provide a path to classically intractable molecular simulation.

VQE and the Active Space Approximation

VQE finds the ground-state energy of a molecular Hamiltonian by optimizing a parameterized quantum circuit (the ansatz) using a classical optimizer in a feedback loop. The circuit prepares a trial state; the quantum device measures its energy expectation value; the classical optimizer updates the parameters.

For drug-relevant molecules, the full electronic Hilbert space is too large for current hardware. The active space approximation selects the chemically important orbitals (those near the HOMO-LUMO gap) and treats only those quantum mechanically. The rest are handled classically.

Pfizer used Qiskit Nature with Jordan-Wigner encoding to map the active space Hamiltonian to qubit operators.

from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import JordanWignerMapper
from qiskit_nature.second_q.circuit.library import UCCSD, HartreeFock
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
from qiskit_algorithms.minimum_eigensolvers import VQE
from qiskit_algorithms.optimizers import SLSQP
from qiskit_aer.primitives import Estimator
import numpy as np

# Define the molecule (hydrogen chain as a tractable proxy for drug fragments)
driver = PySCFDriver(
    atom="H 0 0 0; H 0 0 0.735; H 0 0 1.47; H 0 0 2.205",
    basis="sto-3g",
    charge=0,
    spin=0,
)
problem = driver.run()

# Restrict to active space: 4 electrons in 4 orbitals
transformer = ActiveSpaceTransformer(num_electrons=4, num_spatial_orbitals=4)
active_problem = transformer.transform(problem)

# Map fermionic Hamiltonian to qubit operators via Jordan-Wigner
mapper = JordanWignerMapper()
qubit_op = mapper.map(active_problem.second_q_ops()[0])

print(f"Qubit Hamiltonian has {qubit_op.num_qubits} qubits")
print(f"Number of Pauli terms: {len(qubit_op)}")

# Build UCCSD ansatz initialized at Hartree-Fock reference
num_spatial_orbs = active_problem.num_spatial_orbitals
num_particles = active_problem.num_particles

hf_state = HartreeFock(
    num_spatial_orbitals=num_spatial_orbs,
    num_particles=num_particles,
    qubit_mapper=mapper,
)

ansatz = UCCSD(
    num_spatial_orbitals=num_spatial_orbs,
    num_particles=num_particles,
    qubit_mapper=mapper,
    initial_state=hf_state,
)

# Run VQE using a noiseless statevector estimator
estimator = Estimator()
optimizer = SLSQP(maxiter=300)

vqe = VQE(estimator=estimator, ansatz=ansatz, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(qubit_op)

hartree_energy = active_problem.reference_energy
total_energy = result.eigenvalue.real + hartree_energy

print(f"VQE ground state energy: {result.eigenvalue.real:.6f} Ha")
print(f"Total energy (with nuclear repulsion): {total_energy:.6f} Ha")

Jordan-Wigner Encoding

The Jordan-Wigner transformation converts fermionic creation and annihilation operators into qubit Pauli strings. Each spin-orbital maps to one qubit. For an active space with M spin-orbitals, the qubit count is M.

This is why active space selection is critical: a 50-orbital active site would require 50+ qubits, far beyond current noise budgets. Pfizer’s work focused on rigorously identifying the minimal chemically relevant active space for each drug target.

Benchmarking Against Classical Methods

Pfizer benchmarked VQE results against two classical references:

• Hartree-Fock (HF): The mean-field baseline, fast but ignores electron correlation
• CCSD(T): The coupled-cluster gold standard, accurate but exponentially expensive

For 4-6 qubit test systems (small ligand fragments), VQE with UCCSD ansatz recovered correlation energies within chemical accuracy (1 kcal/mol, approximately 1.6 mHa) of CCSD(T). This validated the quantum workflow end to end.

Results

Key outcomes from the Pfizer-IBM collaboration:

• VQE matched CCSD(T) accuracy on hydrogen chain and small organic fragment test cases using 4-6 qubits
• Jordan-Wigner encoding with UCCSD ansatz produced well-converged results on noise-free simulators
• On real IBM Quantum hardware, error mitigation (zero-noise extrapolation) was necessary to recover accurate energies
• Estimated qubit requirement for a practical drug-protein active site: 1000+ logical qubits with full error correction

The collaboration produced published methodology for active space selection tailored to drug-relevant molecular systems, a contribution that benefits the broader quantum chemistry community independent of hardware timelines.

What Quantum Drug Discovery Needs

Pfizer’s analysis identified the scaling gap clearly. Practically relevant drug-protein simulations require:

1. Logical qubit counts: 1000+ error-corrected qubits for a 50-orbital active site
2. Fault tolerance: Current hardware error rates (~0.1-1% per gate) destroy correlation energy calculations beyond 10-12 qubits without heavy error mitigation
3. Circuit depth: UCCSD ansatz depth grows with system size; shallow hardware limits applicability today

The near-term strategy focuses on using quantum hardware to benchmark and validate active space selection protocols that then feed classical CCSD(T) calculations on affordable subsystems.

IBM Quantum Network Partnership

Pfizer joined the IBM Quantum Network to access premium quantum systems and collaborate directly with IBM’s quantum chemistry team. This partnership provides:

• Early access to new hardware generations
• Collaborative development of Qiskit Nature workflows for pharma
• Joint publication pipeline for methodology papers

The partnership is part of a broader trend of pharmaceutical companies (Pfizer, Roche, Biogen, Merck) establishing formal quantum computing programs alongside their classical computational chemistry groups.

Learn more: Qiskit Nature Reference | VQE Algorithm Guide