Improved output-sensitive quantum algorithms for Boolean matrix multiplication

We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n × n Boolean matrices can be computed on a quantum computer in time ˜O(n3/2 + nℓ3/4 ), where ℓ is the number of non-zero entries in the product, improving over the output-sensitive quantum algorithm by Buhrman and ˇSpalek that runs in ˜O(n3/2 √ ℓ) time. This is done by constructing a quantum version of a recent algorithm by Lingas, using quantum techniques such as quantum counting to exploit the sparsity of the output matrix. As far as query complexity is concerned, our results improve over the quantum algorithm by Vassilevska Williams and Williams based on a reduction to the triangle finding problem. One of the main contributions leading to this improvement is the construction of a triangle finding quantum algorithm tailored especially for the tripartite graphs...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: François Le Gall
• Keywords: Algorithms, Boolean Matrices, Quantum Algorithm, Quantum Algorithms, SODA 2012