Tangible reduction in learning sample complexity with large classical samples and small quantum system

Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources in general. It would therefore be desirable to avoid it, if possible, for noisy intermediate-scale quantum (NISQ) implementation. Accordingly, we consider a classical-quantum hybrid architecture, which allows large classical input data, with a relatively small-scale W. Song Department of Physics, Hanyang University, Seoul 04763, Korea Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea M. Wieśniak Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308 Gdańsk, Poland International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland N. Liu Institute of Natural Science, Shanghai Jiao Tong University, Shanghai 200240, China Ministry of Education, Key Laboratory in Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240, China University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai 200240, China M. Paw lowski International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308 Gdańsk, Poland ?J. Lee (E-mail: hyoung@hanyang.ac.kr) Department of Physics, Hanyang University, Seoul 04763, Korea ?J. Kim (E-mail: jaewan@kias.re.kr) School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea ?J. Bang (E-mail: jbang@etri.re.kr) Electronics and Telecommunications Research Institute, Daejeon 34129, Korea ?Correspondence and requests for materials should be addressed to the last three authors. ar X iv :1 90 5. 05 75 1v 3 [ qu an tph ] 1 S ep 2 02 1 2 Wooyeong Song et al. quantum system. This hybrid architecture is used to implement a sampling oracle. It is shown that in the presence of noise in the hybrid oracle, the effects of internal noise can cancel each other out and thereby improve the query success rate. It is also shown that such an immunity of the hybrid oracle to noise directly and tangibly reduces the sample complexity in the framework of computational learning theory. This NISQ-compatible learning advantage is attributed to the oracle’s ability to handle large input features.

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