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COLT
2010
Springer

Quantum Predictive Learning and Communication Complexity with Single Input

9 years 5 months ago
Quantum Predictive Learning and Communication Complexity with Single Input
We define a new model of quantum learning that we call Predictive Quantum (PQ). This is a quantum analogue of PAC, where during the testing phase the student is only required to answer a polynomial number of testing queries. We demonstrate a relational concept class that is efficiently learnable in PQ, while in any "reasonable" classical model exponential amount of training data would be required. This is the first unconditional separation between quantum and classical learning. We show that our separation is the best possible in several ways; in particular, there is no analogous result for a functional class, as well as for several weaker versions of quantum learning. In order to demonstrate tightness of our separation we consider a special case of one-way communication that we call single-input mode, where Bob receives no input. Somewhat surprisingly, this setting becomes nontrivial when relational communication tasks are considered. In particular, any problem with two-sid...
Dmitry Gavinsky
Added 10 Feb 2011
Updated 10 Feb 2011
Type Journal
Year 2010
Where COLT
Authors Dmitry Gavinsky
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