title: Quantum hyperparallel algorithm for matrix multiplication.
abstract: Hyperentangled states, entangled states with more than one degree of freedom, are considered as promising resource in quantum computation. Here we present a hyperparallel quantum algorithm for matrix multiplication with time complexity O(N(2)), which is better than the best known classical algorithm. In our scheme, an N dimensional vector is mapped to the state of a single source, which is separated to N paths. With the assistance of hyperentangled states, the inner product of two vectors can be calculated with a time complexity independent of dimension N. Our algorithm shows that hyperparallel quantum computation may provide a useful tool in quantum machine learning and "big data" analysis.
authors.affiliation: Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
authors.forename: Xin-Ding
authors.initials: XD
authors.lastname: Zhang
authors.affiliation: Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
authors.forename: Xiao-Ming
authors.initials: XM
authors.lastname: Zhang
authors.affiliation: Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China.
authors.forename: Zheng-Yuan
authors.initials: ZY
authors.lastname: Xue