Inductive Supervised Quantum Learning
Abstract
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the classical setting, from a simple independence requirement with a physical interpretation of being nonsignaling. Thus, two seemingly different definitions of inductive learning happen to coincide. This follows from the properties of classical information that break down in the quantum setup. We prove a quantum de Finetti theorem for quantum channels, which shows that in the quantum case, the equivalence holds in the asymptotic setting, that is, for large numbers of test instances. This reveals a natural analogy between classical learning protocols and their quantum counterparts, justifying a similar treatment, and allowing us to inquire about standard elements in computational learning theory, such as structural risk minimization and sample complexity.
 Publication:

Physical Review Letters
 Pub Date:
 May 2017
 DOI:
 10.1103/PhysRevLett.118.190503
 arXiv:
 arXiv:1605.07541
 Bibcode:
 2017PhRvL.118s0503M
 Keywords:

 Computer Science  Machine Learning;
 Quantum Physics;
 Statistics  Machine Learning
 EPrint:
 6+10 pages