Quantum Quality Control in Additive Manufacturingwith a Trainable QSVM

Metal powder-bed fusion — electron-beam and laser powder-bed fusion (EPBF/LPBF) — builds parts layer by layer from a molten pool of metal, and an unstable melt pool is the root cause behind porosity, lack-of-fusion voids, and rough surfaces. Catching an unstable melt pool late, after a build finishes, means a scrapped part and a repeated build cycle; catching it from in-process signal means a cheaper correction, or a decision to stop a build before it wastes material and machine time. The same melt-pool process data supports two different quality-control questions: is this melt pool behaving normally at all, and, if not, which defect regime is it in. We answer both with the same modeling approach — a Quantum Support Vector Machine (QSVM) with a trainable quantum kernel — applied to two worked cases below: binary anomaly detection and multi-class melt-pool shape classification.

Both cases start from a classical SVM pipeline: the model seeks a separating hyperplane in feature space, \mathbf{w}^\top \phi(\mathbf{x}) + b = 0, maximizing the geometric margin between classes. When linear separation is difficult, we map data to a higher-dimensional space and apply the kernel trick: instead of building \phi(\cdot) explicitly, we compute inner products k(\mathbf{x},\mathbf{x}')=\langle \phi(\mathbf{x}), \phi(\mathbf{x}')\rangle, which lets the SVM operate implicitly in a Hilbert space \mathcal{H}.

The quantum kernel replaces that classical map with a circuit: input \mathbf{x} is encoded into a quantum state |\phi(\mathbf{x})\rangle=U(\mathbf{x})|0\rangle^{\otimes n}, and the state overlap (inner product or fidelity) becomes k(\mathbf{x},\mathbf{x}'). Data-dependent single-qubit rotations and entangling gates induce a nonlinear embedding; the overlaps are estimated by running U(\mathbf{x}')^\dagger U(\mathbf{x}), and the resulting Gram matrix feeds directly into the standard SVM pipeline. Adding trainable parameters \boldsymbol{\theta} to the encoding circuit — used in the anomaly-detection case below — lets the kernel geometry adapt to the data, by maximizing target alignment, minimizing a margin-based surrogate, or reducing cross-validated risk.

Both circuits below use the same shape: 4 qubits and 2 repeated layers of data-dependent rotations and entangling gates. That depth is deliberately shallow — a design choice that keeps the number of two-qubit gates, and with it the accumulated gate error, low enough for the kernel to be evaluated on both a classical simulator and today's noisy quantum hardware, at the cost of a less expressive feature map than a deeper circuit could offer.

Both cases below benchmark the quantum kernel against a classical SVM baseline on the same data. For a same-dataset, side-by-side benchmark of QSVM against a classical kernel SVM, see our QSVM vs. classical SVM comparison.