Quantum kernel inference cuts query cost by removing data-size dependence
New algorithm reduces quantum machine learning inference complexity from O(N) to O(1) in data size, achieving query-optimal bounds via amplitude estimation.
Source: arxiv/cs.LG · Elies Gil-fuster, Seongwook Shin, Sofiene Jerbi, Jens Eisert, Maximilian J. Kramer · open original ↗
Quantum kernel inference can eliminate dependence on training set size N by encoding the full sum as a single observable and using amplitude estimation.
- — Standard inference requires O(N||α||₂²/ε²) queries by estimating each kernel term independently.
- — New approach encodes all kernel terms into one observable, reducing to O(||α||₁/ε) queries.
- — Removes N from query complexity entirely; quadratic gains in coefficient norm and precision.
- — Matching lower bound proves the algorithm is query-optimal up to logarithmic factors.
- — Gate complexity differs from query complexity; practical choice depends on hardware constraints.
- — All methods use amplitude estimation as core subroutine, suitable for near-term quantum devices.
- — Provides landscape of intermediate strategies for practitioners with varying hardware capabilities.
Astrobobo tool mapping
- Knowledge Capture Record the three inference axes: (1) kernel estimation method (sampling vs. amplitude), (2) summation method (term-by-term vs. single observable), (3) your hardware's amplitude estimation fidelity. Use this to map which combination applies to your use case.
- Focus Brief Summarize the query-optimal bound O(||α||₁/ε) and the practical gate-cost trade-off. Note that query-optimality does not guarantee wall-clock speedup on real devices.
- Reading Queue Queue related work on amplitude estimation error propagation and near-term quantum device implementations of kernel methods to understand feasibility gaps.
Frequently asked
- Standard inference queries each of N kernel values independently, costing O(N||α||₂²/ε²) queries. The new method encodes all kernel terms into a single observable and applies quantum amplitude estimation, reducing cost to O(||α||₁/ε). This removes dependence on N entirely and provides quadratic improvements in both the coefficient norm and precision parameters.
cite ▸
APA
Elies Gil-fuster, Seongwook Shin, Sofiene Jerbi, Jens Eisert, Maximilian J. Kramer. (2026, April 17). Quantum kernel inference cuts query cost by removing data-size dependence. Astrobobo Content Engine (rewrite of arxiv/cs.LG). https://astrobobo-content-engine.vercel.app/article/quantum-kernel-inference-cuts-query-cost-by-removing-data-size-dependence-bcf387
MLA
Elies Gil-fuster, Seongwook Shin, Sofiene Jerbi, Jens Eisert, Maximilian J. Kramer. "Quantum kernel inference cuts query cost by removing data-size dependence." Astrobobo Content Engine, 17 Apr 2026, https://astrobobo-content-engine.vercel.app/article/quantum-kernel-inference-cuts-query-cost-by-removing-data-size-dependence-bcf387. Based on "arxiv/cs.LG", https://arxiv.org/abs/2604.15214.
BibTeX
@misc{astrobobo_quantum-kernel-inference-cuts-query-cost-by-removing-data-size-dependence-bcf387_2026,
author = {Elies Gil-fuster, Seongwook Shin, Sofiene Jerbi, Jens Eisert, Maximilian J. Kramer},
title = {Quantum kernel inference cuts query cost by removing data-size dependence},
year = {2026},
url = {https://astrobobo-content-engine.vercel.app/article/quantum-kernel-inference-cuts-query-cost-by-removing-data-size-dependence-bcf387},
note = {Astrobobo rewrite of arxiv/cs.LG, https://arxiv.org/abs/2604.15214},
}