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

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.