Quantum versus classical learnability

Abstract

Abstract

Separating Quantum and Classical Learning

“…This separation between quantum and classical learning is far more robust than previous work [26]. Even if a polynomial-time classical factoring algorithm were to be discovered, our separation would hold as long as any one-way function exists (a universally held belief in public-key cryptography).…”

“…In contrast with the work described above, the goal here is to exactly identify the black-box function rather than to determine whether or not it has some property. Servedio and Gortler [26] defined such a model and proved that any concept class ¡ which is information-theoretically learnable from polynomially many quantum membership queries is also informationtheoretically learnable from polynomially many classical membership queries (they also gave a similar result for the quantum PAC learning model of [10]). …”

“…This result from [26] deals only with query complexity and does not address the computational complexity of quantum versus classical learning. Indeed, [26] also showed that polynomial-time quantum learning is more powerful than polynomial-time classical learning under the assumption that factoring is computationally hard for classical computers.…”

“…Indeed, [26] also showed that polynomial-time quantum learning is more powerful than polynomial-time classical learning under the assumption that factoring is computationally hard for classical computers. This follows directly from the observation that Shor's quantum factoring algorithm enables quantum algorithms to efficiently learn concept classes whose classical learnability is directly related to the hardness of factoring [2,20].…”

“…We consider a model of learning Boolean functions from quantum membership queries. This model was studied in [26], where it was shown that any class of Boolean functions which is information-theoretically learnable from polynomially many quantum membership queries is also information-theoretically learnable from polynomially many classical membership queries. In this paper we establish a strong computational separation between quantum and classical learning.…”