ψQMLQUANTUM MACHINE LEARNING
Chapter 05 / Concept 18 of 48

Quantum support vector machines

Use quantum-derived Gram matrices in classical margin-based SVM optimization.

Input / assumptions→ Quantum or learning model→ Measurement / inference→ Validation

Core idea

Use quantum-derived Gram matrices in classical margin-based SVM optimization. The central design question is what information the representation retains, which operations are physically implementable, and how prediction quality and total resource cost are measured. In QML, a mathematical formulation must be paired with an explicit data-access model and a reproducible evaluation protocol.

$$\max_\alpha\sum_i\alpha_i-\tfrac12\sum_{ij}\alpha_i\alpha_j y_i y_jK_{ij}$$

Worked example

Compute an $N\times N$ kernel matrix then fit an ordinary SVM with a precomputed kernel.

How to study or implement it

Start with a minimal analytic case that can be checked by hand. Build a noiseless simulation, inspect intermediate states or predictions, and then repeat with finite sampling. Compare against a suitable classical reference using the same dataset, preprocessing, and evaluation split. Record circuit depth, qubit count, optimization steps, and measurement budget.

Interpretation and limitations

Kernel matrix estimation costs grow at least quadratically with sample count for a full matrix. When evaluating experimental claims, separate theoretical asymptotic statements from measured end-to-end performance. Include preprocessing, state preparation, parameter tuning and output extraction in the comparison.

Further exploration

See the chapter overview, interactive lab, guided learning path, and curated sources.

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