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2012
ACM

Improved output-sensitive quantum algorithms for Boolean matrix multiplication

7 years 2 months ago
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...
François Le Gall
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where SODA
Authors François Le Gall
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