Optimal algorithmic complexity of inference in quantum kernel methods
Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum $\sum_{i=1}^N α_i k(x,x_i)$ of $N$ kernel values to additive precision $\varepsilon$, where $α$ is the vector of trained coefficients. The standard approach estimates each term independently via sampling, yielding a query complexity of $O(N\lVertα\rVert_2^2/\varepsilon^2)$. In this work, we identify two independent axes for improvement: (1) How individual kernel values are estimated (sampling versus quantum amplitude estimation), and (2) how the sum is approximate...
| Authors | Elies Gil-Fuster, Seongwook Shin, Sofiene Jerbi et al. |
|---|---|
| Primary category | quant-ph |
| Published | 16 April 2026 |
| Last updated at source | 17 April 2026 |
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