Universal Matrix Multiplication on Quantum Computer

TL;DR

This paper introduces a practical universal quantum matrix multiplication method using optimized quantum adders and multipliers, demonstrating potential for accelerating machine learning computations on quantum computers.

Contribution

It presents the first reliable design of universal quantum matrix multiplication and extends it to the Strassen algorithm, with experimental validation of performance improvements.

Findings

Quantum adders and multipliers significantly reduce gate count.

Quantum matrix multiplication shows notable speedup over classical methods.

Quantum Strassen algorithm offers advantages in efficiency.

Abstract

As a core underlying operation in pattern recognition and machine learning, matrix multiplication plays a crucial role in modern machine learning models and constitutes a major contributor to computational expenditure. Hence, researchers have spent decades continuously searching for more efficient matrix multiplication algorithms.This paper firstly introduces an innovative and practical approach to universal quantum matrix multiplication. We designed optimized quantum adders and multipliers based on Quantum Fourier Transform (QFT), which significantly reduced the number of gates used compared to classical adders and multipliers. Subsequently, we construct the basic universal quantum matrix multiplication and extend it to the Strassen algorithm. We conduct comparative experiments to analyze the performance of the quantum matrix multiplication and evaluate the acceleration provided by the optimized quantum adder and multiplier. Finally, we investigate the advantages of the quantum Strassen algorithm and the basic quantum matrix multiplication. Our result opens, for the first time, a reliable pathway for designing universal quantum matrix multiplication. Following this pathway, quantum computing will unlock significantly greater potential for training modern machine learning models.