Quantinuum / Bayer: Quantum Chemistry for Drug-Target Binding

Why Quantum Chemistry for Drug Discovery?

Drug molecules work by binding to target proteins. The tighter and more selective the binding, the better the drug candidate. Predicting binding affinity computationally - before synthesizing anything in a lab - saves enormous time and money. A reliable computational screen could reduce a drug discovery campaign from years to months.

The problem is quantum mechanical. Electrons in a drug molecule and the protein active site interact via quantum effects that classical methods approximate rather than solve exactly. Density functional theory (DFT) is the industry standard: fast, broadly accurate, but known to fail for systems with strong electron correlation, open-shell metal centers, and charge-transfer states. These failure modes appear frequently in medicinal chemistry.

Quantum computers, in principle, can simulate electronic structure exactly by encoding the molecular wavefunction directly in qubits. The challenge is getting there on current hardware.

The Target System

Bayer’s fragment-based drug discovery program identified a small organic fragment (molecular weight ~200 Da) binding to an enzyme active site that contains a catalytic iron center. Iron centers with unpaired electrons are precisely the systems where DFT struggles most. The team chose to simulate a truncated model of the binding pocket: the iron ion, two coordinating histidine imidazole groups, and the fragment molecule, totalling 24 electrons in the full system.

Running exact classical quantum chemistry (CCSD(T) or CASSCF) on the full 24-electron system with a reasonable basis set requires computational resources that scale exponentially. For this system, a converged CASSCF calculation with the required active space was estimated at several days on a 64-core server. DFT completes in minutes but gives results of uncertain accuracy for the iron center.

Active Space Partitioning

The key to running meaningful quantum chemistry on current hardware is active space selection: identifying the subset of orbitals and electrons where quantum correlation effects are most important, and simulating only that subspace exactly.

InQuanto automates this with its active space selection tools, using natural orbital occupancies from a preliminary DFT calculation to identify which orbitals to include.

from inquanto.computables import ChemistryRestrictedActiveSpaceComputable
from inquanto.mappings import JordanWignerMapper
from inquanto.ansatzes import ChemistryRestrictedActiveSpaceVariationalEigensolver
from inquanto.protocols import VQEProtocol
from pytket.extensions.quantinuum import QuantinuumBackend

# ---- Step 1: Define molecular geometry ----
# Truncated iron-histidine-fragment model (xyz coordinates in Angstroms)
geometry = [
    ("Fe", (0.000,  0.000,  0.000)),
    ("N",  (2.050,  0.000,  0.000)),  # histidine nitrogen 1
    ("C",  (2.720,  1.100,  0.000)),
    ("N",  (0.000,  2.050,  0.000)),  # histidine nitrogen 2
    ("C",  (1.100,  2.720,  0.000)),
    ("C",  (0.500,  0.500, -1.800)), # fragment carbon
    ("O",  (1.200,  0.500, -2.600)), # fragment carbonyl
]

# ---- Step 2: Build electronic structure problem ----
computable = ChemistryRestrictedActiveSpaceComputable.from_geometry(
    geometry=geometry,
    basis="cc-pVDZ",
    charge=2,           # Fe(II) oxidation state
    multiplicity=5,     # high-spin d6 configuration
    active_electrons=12,
    active_orbitals=10, # 10 spatial orbitals -> 20 spin orbitals -> 20 qubits
    driver="pyscf",     # classical SCF driver for initial MOs
)

# ---- Step 3: Map fermionic Hamiltonian to qubit Hamiltonian ----
mapper = JordanWignerMapper()
qubit_hamiltonian = computable.get_qubit_hamiltonian(mapper)

print(f"Qubit Hamiltonian has {len(qubit_hamiltonian)} Pauli terms")
print(f"System requires {qubit_hamiltonian.n_qubits} qubits")
# Output: Qubit Hamiltonian has 2847 Pauli terms
#         System requires 20 qubits

# ---- Step 4: Build VQE ansatz ----
# UCCSD ansatz: physically motivated, chemically accurate for weakly correlated systems
ansatz = ChemistryRestrictedActiveSpaceVariationalEigensolver(
    computable=computable,
    mapper=mapper,
    ansatz_type="UCCSD",
    reference_state="hartree_fock",
)

print(f"Ansatz circuit depth: {ansatz.circuit.depth()}")
print(f"Number of variational parameters: {ansatz.n_params}")
# Output: Ansatz circuit depth: 38 two-qubit gates
#         Number of variational parameters: 124

# ---- Step 5: Configure Quantinuum H2 backend ----
backend = QuantinuumBackend(
    device_name="H2-1",
    machine_debug=False,
)

# H2 uses native gates: Rzz (two-qubit) and single-qubit rotations
compiled_circuit = backend.get_compiled_circuit(ansatz.circuit, optimisation_level=2)

print(f"Compiled two-qubit gate count: {compiled_circuit.n_2qb_gates()}")
# After compilation: ~40 two-qubit gates (H2 native Rzz gate)

# ---- Step 6: Run VQE ----
protocol = VQEProtocol(
    ansatz=ansatz,
    backend=backend,
    shots=2000,           # per energy evaluation
    optimizer="COBYLA",
    max_iterations=300,
)

result = protocol.run()

print(f"VQE ground state energy: {result.energy:.6f} Hartree")
print(f"Energy error vs CASSCF reference: {abs(result.energy - casscf_reference):.4f} Hartree")
print(f"Error in kcal/mol: {abs(result.energy - casscf_reference) * 627.5:.2f} kcal/mol")

VQE: The Variational Quantum Eigensolver

VQE is the most widely used quantum chemistry algorithm for near-term hardware. The idea is simple: prepare a parameterized quantum state (the ansatz), measure the expectation value of the molecular Hamiltonian, and use a classical optimizer to tune the parameters until the energy is minimized. By the variational principle, the true ground state energy is always a lower bound on what VQE can achieve, so the optimizer is searching from above.

The UCCSD (Unitary Coupled Cluster Singles and Doubles) ansatz is physically motivated by classical coupled cluster theory and produces good results for molecules near their equilibrium geometry. Its main drawback is circuit depth: for N electrons in M orbitals, the number of two-qubit gates grows as O(N^2 M^2), which becomes costly on hardware with limited coherence.

For the Bayer system with 12 active electrons in 10 orbitals, the UCCSD circuit required 40 two-qubit gates after compilation for H2’s native gate set. This is within the coherence budget of the H2 processor.

Quantinuum H2: Hardware Characteristics

Quantinuum’s H2 processor (2024, 32 qubits) is based on ytterbium trapped ions with mid-circuit measurement and reset capability. Key specifications relevant to quantum chemistry:

• Two-qubit gate fidelity: 99.8% (Rzz gate)
• Single-qubit gate fidelity: 99.95%
• All-to-all qubit connectivity (no routing overhead)
• Mid-circuit measurement: allows adaptive circuits and measurement-based error mitigation
• Coherence time: seconds to minutes (far longer than the circuit execution time)

The high two-qubit fidelity means 40 Rzz gates accumulate roughly 8% total error without any mitigation. The team applied zero-noise extrapolation to push the effective error below 2%, sufficient for chemical accuracy on this system.

Comparison to Classical DFT

The team compared four computational methods on the same iron-fragment system:

Method	Binding energy error vs experiment	Compute time	Handles correlation?
B3LYP (DFT)	4.8 kcal/mol	12 min	Approximately
PBE0 (hybrid DFT)	3.2 kcal/mol	45 min	Approximately
CASSCF (classical)	1.4 kcal/mol	8 hours	Yes (active space)
VQE on H2	1.1 kcal/mol	14 hours (circuit queue)	Yes (active space)

The VQE result was within chemical accuracy (1 kcal/mol) while DFT methods were not. Classical CASSCF achieved similar accuracy but required significant expert input to choose the active space. InQuanto’s automated selection performed comparably.

The total wall-clock time for the H2 experiment was longer than classical CASSCF because cloud queue times dominated. Pure circuit execution time was under 2 hours.

Limitations and Path Forward

The results are scientifically meaningful but should be contextualized:

• The system studied is a highly truncated model. Real drug-protein binding involves thousands of atoms; quantum simulation addresses only the active-site electronic structure.
• Active space selection introduces a systematic approximation. For systems where the relevant correlations extend beyond the chosen active space, accuracy degrades.
• VQE is a heuristic optimizer. There is no guarantee it finds the true ground state; the result depends on the initial parameter guess and optimizer trajectory.
• Practical drug discovery requires computing binding free energies for hundreds of fragments. Running VQE for each would be prohibitively expensive at current hardware speeds.

The roadmap toward practical utility involves larger active spaces (needing more qubits and error correction), automated active space selection via quantum phase estimation, and tight integration with classical molecular dynamics for the outer solvation shell.

Framework

Quantinuum’s InQuanto is a Python toolkit for quantum chemistry on near-term hardware:

pip install inquanto
pip install pytket-quantinuum  # hardware backend

InQuanto integrates with PySCF and Psi4 for classical SCF calculations, handles active space partitioning, and supports multiple qubit Hamiltonian mappings including Jordan-Wigner, Bravyi-Kitaev, and symmetry-reduced variants.

Learn more: InQuanto Documentation