Analysis of Quantum Computing Resources in the Implementation of the Quantum Fourier Transform and Grover Algorithm on Qudit Systems

The effectiveness of the implementation of the quantum Fourier transform (QFT) and the Grover algorithm on qudit systems is investigated. A comparative analysis of computing resources for quantum states of N ≥ 1024 dimension is carried out. It is shown that using qudits can significantly reduce the number of quantum operations in Grover’s algorithm compared to its qubit counterparts, while for QFT the main advantage is to reduce the number of physical carriers. The effect of noise using the Monte Carlo method on the accuracy of algorithms for qubit systems of various dimensions is analyzed.