Optimal Quantum-Classical Separations for Exact Learning
We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonical quantum speedups in this model are witnessed by Grover search and Bernstein-Vazirani, leading to the longstanding conjecture $$ \mathsf{R}(\mathcal C)=O(\mathsf{Q}(\mathcal C)^2+\mathsf{Q}(\mathcal C)\log N). $$ We first refute this conjecture by constructing concept classes $\mathcal C$ and $\mathcal C'$ satisfying \[ \mathsf{R}(\mathcal C)=Ω\!\left(\frac{\mathsf{Q}(\mat...
| Authors | Srinivasan Arunachalam, Amin Shiraz Gilani, Nikhil S. Mande |
|---|---|
| Primary category | quant-ph |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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