Simulation and analysis of quantum phase estimation algorithm in the presence of incoherent quantum noise channels

TL;DR

This paper investigates how incoherent quantum noise affects the performance of the quantum phase estimation algorithm, revealing exponential and linear dependencies of eigenvalue estimation accuracy on noise parameters.

Contribution

It models various incoherent noise channels and analyzes their impact on QPE, providing insights into noise tolerance and error scaling in quantum algorithms.

Findings

Eigenvalue standard deviation depends exponentially on error probability.

Standard deviation increases linearly with qubit number at low error rates.

Different noise models have distinct effects on QPE accuracy.

Abstract

The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in running QPE and other quantum algorithms is the noise in quantum computers. In the present work, we study the impact of incoherent noise on QPE, modeled as trace-preserving and completely positive quantum channels. Different noise models such as depolarizing, phase flip, bit flip, and bit-phase flip are taken to understand the performance of the QPE in the presence of noise. The simulation results indicate that the standard deviation of the eigenvalue of the unitary operator has strong exponential dependence upon the error probability of individual qubits. However, the standard deviation increases only linearly with the number of qubits for fixed error probability when that error probability is small.