The influence of quantum noise on the Grover algorithm and quantum Fourier transform: quantum operations theory approach

TL;DR

This paper develops an analytical approach to model how quantum noise affects the accuracy of multiqubit quantum algorithms like Grover's and Fourier transform, aligning well with Monte Carlo simulations.

Contribution

It introduces a noise modeling method for multiqubit circuits and derives formulas predicting algorithm accuracy degradation due to noise.

Findings

Analytical formulas match Monte Carlo simulation results.

Quantum noise significantly impacts algorithm accuracy.

The approach enables prediction of noise effects in quantum systems.

Abstract

The method of noisy multiqubit quantum circuits modeling is proposed. The analytical formulas for the dependence of quantum algorithms accuracy on qubits count and noise level are obtained for Grover algorithm and quantum Fourier transform. It is shown that the proposed approach is very much in line with results obtained by Monte Carlo statistical modeling method. The developed theory makes it possible to predict the influence of quantum noise on the accuracy of the forward-looking multiqubit quantum systems under development.