Name
Abstract | ||
|---|---|---|
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, CCCu002715). Our main tool is an improvement of Changu0027s lemma for the special case of sparse 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 $Oleft(frac{Q^2}{log Q}log|mathcal{C}|right)$ classical membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMPu002704) by a $log Q$-factor. |
Year | Venue | Field |
|---|---|---|
2018 | arXiv: Quantum Physics | Boolean function,Discrete mathematics,Quantum,Concept class,Quantum computer,Mathematics,Lemma (mathematics),Special case |
DocType | Volume | Citations |
Journal | abs/1810.00481 | 2 |
PageRank | References | Authors |
0.36 | 16 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Srinivasan Arunachalam | 1 | 40 | 5.96 |
| Sourav Chakraborty | 2 | 381 | 49.27 |
| Troy Lee | 3 | 276 | 28.96 |
| Ronald de Wolf | 4 | 144 | 12.34 |