A time-efficient output-sensitive quantum algorithm for Boolean matrix multiplication

Abstract

This paper presents a quantum algorithm that computes the product of two nxn Boolean matrices in Õ(n√ℓ+ℓ√n) time, where ℓ is the number of non-zero entries in the product. This improves the previous output-sensitive quantum algorithms for Boolean matrix multiplication in the time complexity setting by Buhrman and Špalek (SODA'06) and Le Gall (SODA'12). We also show that our approach cannot be further improved unless a breakthrough is made: we prove that any significant improvement would imply the existence of an algorithm based on quantum search that multiplies two nxn Boolean matrices in O(n5/2-ε) time, for some constant ε > 0. © Springer-Verlag 2012.