Improved Bounds on Quantum Learning Algorithms
Quantum Information Processing
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
An improved lower bound on query complexity for quantum PAC learning
Information Processing Letters
Exact quantum lower bound for grover's problem
Quantum Information & Computation
How many query superpositions are needed to learn?
ALT'06 Proceedings of the 17th international conference on Algorithmic Learning Theory
Machine learning in a quantum world
AI'06 Proceedings of the 19th international conference on Advances in Artificial Intelligence: Canadian Society for Computational Studies of Intelligence
Random oracles in a quantum world
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Quantum predictive learning and communication complexity with single input
Quantum Information & Computation
Quantum adiabatic machine learning
Quantum Information Processing
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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 or classical queries required for learning. These results contrast known results that show that testing black-box functions for various properties, as opposed to learning, can require exponentially more classical queries than quantum queries. We also show that, under a widely held computational hardness assumption (the intractability of factoring Blum integers), 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. For the model of exact learning from membership queries, we establish a stronger separation by showing that if any one-way function exists, then there is a class of functions which is polynomial-time learnable in the quantum setting but not in the classical setting. Thus, while quantum and classical learning are equally powerful from an information theory perspective, the models are different when viewed from a computational complexity perspective.