Reference Work Entry

Encyclopedia of Algorithms

pp 1673-1677

Date:

Quantum Algorithms for Matrix Multiplication and Product Verification

  • Robin KothariAffiliated withCenter for Theoretical Physics, Massachusetts Institute of TechnologyDavid R. Cheriton School of Computer Science, Institute for Quantum Computing, University of Waterloo Email author 
  • , Ashwin NayakAffiliated withDepartment of Combinatorics and Optimization, Institute for Quantum Computing, University of Waterloo

Keywords

Boolean matrix multiplication Matrix product verification Quantum algorithms

Years and Authors of Summarized Original Work

  • 2006; Buhrman, Špalek

  • 2012; Jeffery, Kothari, Magniez

Problem Definition

Let S be any algebraic structure over which matrix multiplication is defined, such as a field (e.g., real numbers), a ring (e.g., integers), or a semiring (e.g., the Boolean semiring). If we use + and ⋅ to denote the addition and multiplication operations over S, then the matrix product C of two n × n matrices A and B is defined as ...

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