Lockheed Martin: Quantum Simulation for Aerospace Materials

The Problem

Aerospace materials are engineered at the quantum level. The structural strength of carbon fiber composites, the electromagnetic properties of radar-absorbing coatings, and the heat tolerance of turbine alloys all arise from quantum mechanical interactions between atoms and electrons.

Classical simulation of these materials requires solving the many-body Schrodinger equation, which scales exponentially with the number of electrons. Density functional theory (DFT) approximates this but fails for strongly correlated materials where electron-electron interactions dominate. These strongly correlated systems, including magnetic alloys and superconductors relevant to aerospace applications, are precisely where quantum computers are expected to offer genuine speedup.

From D-Wave to Gate-Based Hardware

Lockheed Martin’s quantum computing history is longer than most. In 2010, the company purchased a D-Wave One system alongside the University of Southern California, one of the first commercial quantum computing installations in the world.

That D-Wave system was not used for materials simulation. Quantum annealers solve optimization problems, not simulation problems. Lockheed applied it to software verification tasks: finding bugs in flight control system code by formulating the problem as combinatorial search. This was a genuine use case, not a demonstration, but it was distinct from the materials simulation goal.

For quantum simulation of materials, Lockheed shifted to gate-based research. Partnerships with IBM and IonQ focused on simulating Heisenberg spin models, quantum mechanical abstractions that capture the magnetic behavior of real materials.

Heisenberg Spin Chain Simulation

The Heisenberg model describes a chain of quantum spins (each a qubit) interacting with their neighbors. The Hamiltonian for a chain of N spins is:

H = J * sum( X_i X_{i+1} + Y_i Y_{i+1} + Z_i Z_{i+1} )

Simulating this model’s ground state and dynamics tests the same techniques needed for real materials but at tractable scale. On a 2-qubit chain:

from qiskit import QuantumCircuit
from qiskit.primitives import Estimator
from qiskit.quantum_info import SparsePauliOp
from qiskit_algorithms import VQE
from qiskit_algorithms.optimizers import COBYLA
import numpy as np

# 2-qubit Heisenberg Hamiltonian: H = J*(XX + YY + ZZ)
J = 1.0
hamiltonian = SparsePauliOp.from_list([
    ("XX", J),
    ("YY", J),
    ("ZZ", J),
])

# Ansatz: parameterized circuit to approximate ground state
def heisenberg_ansatz(theta):
    qc = QuantumCircuit(2)
    # Initial Bell-like state preparation
    qc.ry(theta[0], 0)
    qc.ry(theta[1], 1)
    qc.cx(0, 1)
    qc.ry(theta[2], 0)
    qc.ry(theta[3], 1)
    return qc

from qiskit.circuit import ParameterVector
params = ParameterVector("theta", 4)
ansatz = QuantumCircuit(2)
ansatz.ry(params[0], 0)
ansatz.ry(params[1], 1)
ansatz.cx(0, 1)
ansatz.ry(params[2], 0)
ansatz.ry(params[3], 1)

# Run VQE to find ground state energy
estimator = Estimator()
optimizer = COBYLA(maxiter=300)
vqe = VQE(estimator=estimator, ansatz=ansatz, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(hamiltonian)

print(f"VQE ground state energy: {result.eigenvalue:.4f}")
# Exact result for 2-site Heisenberg: -3J = -3.0 for antiferromagnetic coupling
print(f"Exact ground state energy: {-3 * J:.4f}")

# Time evolution: simulate spin dynamics
from qiskit.circuit.library import PauliEvolutionGate
from qiskit.synthesis import LieTrotter

evolution_gate = PauliEvolutionGate(hamiltonian, time=0.5,
                                    synthesis=LieTrotter(reps=3))
evo_circuit = QuantumCircuit(2)
evo_circuit.h(0)   # Start from superposition
evo_circuit.append(evolution_gate, [0, 1])
evo_circuit.measure_all()
print("Evolution circuit depth:", evo_circuit.decompose().depth())

Why Trapped Ion Hardware

Lockheed’s gate-based research targeted IonQ’s trapped ion hardware for a specific reason: connectivity. Heisenberg model simulation requires applying two-qubit gates between interacting spins. Superconducting processors (like IBM’s) have limited nearest-neighbor connectivity; simulating a spin chain requires SWAP gates to route interactions, increasing circuit depth and error.

Trapped ion systems offer all-to-all connectivity: any qubit can directly interact with any other. For spin models where every site potentially interacts with every other, this is a significant advantage. IonQ’s higher gate fidelities also reduce the error mitigation overhead needed to get clean simulation results.

Results and Roadmap

Lockheed’s published work demonstrated ground state energy calculations for small Heisenberg chains (2-4 sites) on trapped ion hardware, with results matching classical exact diagonalization within error bars after mitigation.

The path to industrially relevant materials simulation is long:

• Near term (1-5 years): Simulate 10-20 site models; validate against classical approximations for simple magnetic materials
• Medium term (5-10 years): Simulate models large enough to test predictions against experiment for targeted material classes
• Long term (10+ years): Fault-tolerant simulation of aerospace-relevant alloys and coatings with quantitative accuracy

Lockheed’s early investment in both annealing and gate-based hardware gives it a broader view of the quantum landscape than most aerospace companies, and positions it to exploit hardware improvements as they arrive.

Framework

Gate-based research used Qiskit for circuit construction and execution, targeting IonQ hardware via cloud access. D-Wave Ocean SDK was used for earlier optimization work.

Learn more: Qiskit Reference