Quantum hyperparallel algorithm for matrix multiplication

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.