This paper introduces a framework for quantum exact learning via queries, the so-called quantum protocol. It is shown that usual protocols in the classical learning setting have quantum counterparts. A combinatorial notion, the general halving dimension, is also introduced. Given a quantum protocol and a target concept class, the general halving dimension provides lower and upper bounds on the number of queries that a quantum algorithm needs to learn. For usual protocols, the lower bound is also valid even if only involution oracle teachers are considered. Under some protocols, the quantum upper bound improves the classical one. The general halving dimension also approximates the query complexity of ordinary randomized learners. From these bounds we conclude that quantum devices can allow moderate improvements on the query complexity. However, any quantum polynomially query learnable concept class must be also polynomially learnable in the classical setting. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Castro, J. (2006). How many query superpositions are needed to learn? In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4264 LNAI, pp. 78–92). Springer Verlag. https://doi.org/10.1007/11894841_10
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