How many queries are needed to learn?
Journal of the ACM (JACM)
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the Power of Quantum Computation
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Learning DNF over the Uniform Distribution Using a Quantum Example Oracle
SIAM Journal on Computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Machine Learning
Machine Learning
A General Dimension for Exact Learning
COLT '01/EuroCOLT '01 Proceedings of the 14th Annual Conference on Computational Learning Theory and and 5th European Conference on Computational Learning Theory
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
How Many Queries Are Needed to Learn One Bit of Information?
Annals of Mathematics and Artificial Intelligence
Equivalences and Separations Between Quantum and Classical Learnability
SIAM Journal on Computing
Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
Logical reversibility of computation
IBM Journal of Research and Development
The geometry of quantum learning
Quantum Information Processing
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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.