Noise-Adaptive Hybrid Variational Quantum Circuits for Industrial Bearing Fault Diagnosis

Variational quantum classifiers lose accuracy on noisy hardware because every noisy layer contracts the measured expectation values toward a fixed point, which shrinks the decision margin relative to the finite-shot measurement uncertainty and, for non-unital channels, biases the readout. A fault-diagnosis circuit trained noiselessly and deployed on such a device therefore degrades in a way that depends on its depth, its encoding and the noise type. This paper proposes a noise-adaptive hybrid variational quantum circuit (NA-VQC) for rolling-element bearing fault classification that measures the noise it will face and sets its own structure before training: single-qubit calibration circuits recover the channel strength, least-squares regression over random Clifford instances of the ansatz estimates the circuit-level readout contraction and bias, kernel-target alignment of the noisy encoding fixes the encoding scale, a contraction-weighted margin criterion derived from a finite-shot flip bound fixes the depth, the circuit is trained under the estimated channel, and an affine readout correction can be refreshed when the noise drifts. A physics-based vibration simulator with the geometry of the SKF 6205 bearing provides a four-class data set at zero-decibel signal-to-noise ratio, from which twelve time-domain and envelope-spectrum features are projected onto four qubits. An exact density-matrix simulator with adjoint gradients, verified against Qiskit Aer to machine precision, evaluates local depolarizing and amplitude-damping channels at 256, 1024 and unlimited measurement shots. The circuit-level contraction is shown to fall well below the single-qubit estimate once entangling gates are present, which explains why naive calibration fails. Across the noise sweep NA-VQC stays within four percentage points of a support vector machine on the same features where the standard pipeline falls to chance, and the depth rule avoids the depths at which accuracy collapses while forgoing at most two points against an exhaustive sweep. Negative findings, including the noise insensitivity of the encoding-scale selection and the redundancy of readout calibration under matched training noise, are reported with their causes.