BAE Systems: Quantum-Enhanced Radar Signal Processing

The Challenge

Modern radar systems operating in contested electromagnetic environments face a core statistical problem: extracting weak target returns from noise. The received signal at a radar receiver is a superposition of genuine target reflections, clutter from terrain or sea surface, and electronic interference. Classical detection relies on matched filtering, which correlates the received signal against a known waveform template to maximise signal-to-noise ratio before applying a threshold detector.

The difficulty arises when target density increases. In dense multi-target scenarios such as air-defence radar tracking dozens of aircraft in close proximity, matched filtering must be applied across a large range-Doppler search grid. Each cell requires an independent statistical test, and the number of cells scales with radar bandwidth and coherent processing interval. For modern wideband radars, the search space reaches tens of millions of cells per scan. Classical processing pipelines handle this with dedicated signal processors, but computational latency grows with scene complexity.

BAE Systems Applied Intelligence investigated whether quantum amplitude estimation could accelerate the statistical detection step, specifically the computation of detection probability across candidate target cells. The question was whether quantum speedup in estimating signal amplitudes could translate into measurable reduction in the number of radar pulses required to achieve a given detection probability against a given false alarm rate.

The Quantum Approach

The detection problem was framed as an amplitude estimation task. For a candidate target cell with complex return amplitude $a$, the detection probability under a Neyman-Pearson test is a function of $|a|^2$ relative to the noise floor. Classically, estimating $|a|^2$ from $N$ independent radar pulses converges as $O(1/\sqrt{N})$. Quantum amplitude estimation (QAE) achieves $O(1/N)$ convergence using a quantum circuit that encodes the signal amplitude as a rotation angle and extracts it via quantum phase estimation.

The radar return amplitude was encoded into a two-qubit rotation, with the Grover-like QAE operator iteratively amplifying the target amplitude state. Qiskit’s AmplitudeEstimation class was used to build the estimation circuit, with the number of evaluation qubits controlling the resolution of the amplitude estimate.

import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit_algorithms import AmplitudeEstimation, EstimationProblem
from qiskit.primitives import Sampler

def build_radar_oracle(signal_amplitude: float) -> QuantumCircuit:
    """
    Encode a normalised radar signal amplitude into a rotation circuit.
    signal_amplitude: float in [0, 1] representing |a| / noise_floor
    """
    theta = 2 * np.arcsin(signal_amplitude)
    qc = QuantumCircuit(1)
    qc.ry(theta, 0)
    return qc

# Target signal amplitude (normalised, SNR = 3 dB -> amplitude ~ 0.707)
target_amplitude = 0.707

state_preparation = build_radar_oracle(target_amplitude)
grover_op = build_radar_oracle(target_amplitude)
grover_op.ry(-2 * 2 * np.arcsin(target_amplitude), 0)  # reflection

problem = EstimationProblem(
    state_preparation=state_preparation,
    objective_qubits=[0],
    grover_operator=grover_op,
)

# 6 evaluation qubits -> 64 amplitude bins, resolution 1/64
ae = AmplitudeEstimation(num_eval_qubits=6, sampler=Sampler())
result = ae.estimate(problem)

estimated_amplitude = np.sqrt(result.estimation)
print(f"True amplitude:      {target_amplitude:.4f}")
print(f"Estimated amplitude: {estimated_amplitude:.4f}")
print(f"Samples used:        {2**6} (vs ~4000 classical pulses for same precision)")

The circuit was benchmarked against a classical matched filter using simulated radar returns at varying SNR levels, measuring the number of signal samples required to reach 90% detection probability at a false alarm rate of $10^{-6}$.

Results and Implications

At SNR levels between 0 and 6 dB, quantum amplitude estimation reached the target detection performance using 40% fewer signal samples than classical matched filtering. The quadratic convergence advantage was most pronounced at low SNR, where classical estimators require the greatest number of pulses to accumulate sufficient statistics. This reduction in required dwell time has direct operational significance: radars can either revisit targets more frequently within a fixed scan rate, or reduce their transmission power for a given detection requirement.

The study was conducted on IBM Quantum hardware using up to 10-qubit circuits, with noise mitigation applied via zero-noise extrapolation. Hardware noise degraded the theoretical convergence advantage; error rates on current devices reduce the effective speedup to approximately 1.5x rather than the theoretical quadratic. However, BAE Systems’ analysis identified that fault-tolerant devices with logical error rates below $10^{-4}$ would recover the full advantage.

For multi-target environments with hundreds of simultaneous detections, the quantum approach offers additional structural benefits: the amplitude estimation operator can be applied in superposition across multiple range-Doppler cells in a single circuit execution, a capability with no direct classical analogue. This suggests quantum radar signal processing is a credible long-horizon application as hardware matures, with initial deployment likely in post-processing workflows rather than real-time tracking loops.