Quantum Algorithms for Matrix Operations Based on Unitary Transformations and Ancillary State Measurements

TL;DR

This paper develops quantum algorithms for matrix operations such as row addition, swapping, trace calculation, and transpose, utilizing multi-qubit Toffoli gates and single-qubit operations, with an analysis of their complexities.

Contribution

It introduces new quantum algorithms for fundamental matrix operations based on unitary transformations and ancillary state measurements, with detailed complexity analysis.

Findings

Quantum algorithms for row addition, swapping, trace, transpose developed

Complexity analysis provided for each quantum matrix operation

Utilizes multi-qubit Toffoli gates and single-qubit operations

Abstract

MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix operations of row addition, row swapping, trace calculation and transpose are obtained. In particular, the complexities of these quantum algorithms are presented, too.