Two new results about quantum exact learning
We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves over the bound of $\widetilde{\Theta}(kn)$ uniformly random $c...
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| Autores principales: | , , , , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/8200064c8301448c9fed6779fd3e55be |
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| Sumario: | We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves over the bound of $\widetilde{\Theta}(kn)$ uniformly random $classical$ examples (Haviv and Regev, CCC'15). Additionally, we provide a possible direction to improve our $\widetilde{O}(k^{1.5})$ upper bound by proving an improvement of Chang's lemma for $k$-Fourier-sparse Boolean functions. Second, we show that if a concept class $\mathcal{C}$ can be exactly learned using $Q$ quantum membership queries, then it can also be learned using $O\left(\frac{Q^2}{\log Q}\log|\mathcal{C}|\right)$ $classical$ membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMP'04) by a $\log Q$-factor. |
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