# Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

# Quantum Algorithms for Matrix Multiplication and Product Verification

• Robin Kothari
• Ashwin Nayak
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_303

## 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 $$C_{ij} :=\sum \nolimits_{ k=1}^{n}A_{ik} \cdot B_{kj}$$

## Keywords

Boolean matrix multiplication Matrix product verification Quantum algorithms
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