Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Separating Quantum and Classical Learning
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Quantum DNF Learnability Revisited
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Quantum inductive inference by finite automata
Theoretical Computer Science
The geometry of quantum learning
Quantum Information Processing
Nonadaptive quantum query complexity
Information Processing Letters
Quantum search of partially ordered sets
Quantum Information & Computation
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Abstract: Motivated by recent work on quantum black-box query complexity, we consider quantum versions of two well-studied models of learning Boolean functions: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. For each of these two learning models we establish a polynomial relationship between the number of quantum versus classical queries required for learning. Our results provide an interesting contrast to known results which show that testing black-box functions for various properties can require exponentially more classical queries than quantum queries. We also show that under a widely held computational hardness assumption there is a class of Boolean functions which is polynomial-time learnable in the quantum version but not the classical version of each learning model; thus while quantum and classical learning are equally powerful from an information theory perspective, they are different when viewed from a computational complexity perspective.