Impact of Temporally Correlated Dephasing Noise on the Fidelity of the 2-Qubit Deutsch-Jozsa Algorithm

TL;DR

This study examines how realistic, temporally correlated dephasing noise affects the fidelity of the 2-qubit Deutsch-Jozsa algorithm, revealing non-monotonic effects and limitations of Markovian approximations.

Contribution

It models non-Markovian dephasing noise using the Ornstein-Uhlenbeck process and analyzes its impact on quantum algorithm fidelity through numerical simulations.

Findings

Fidelity varies non-monotonically with noise correlation time.

Markovian models only accurately predict fidelity at very short correlation times.

Longer correlation times lead to overestimation of fidelity by Markovian approximations.

Abstract

Understanding the influence of realistic noise on quantum algorithms is paramount for the advancement of quantum computation. While often modeled as Markovian, environmental noise in quantum systems frequently exhibits temporal correlations, leading to non-Markovian dynamics that can significantly alter algorithmic performance. This paper investigates the impact of temporally correlated dephasing noise, modeled by the Ornstein-Uhlenbeck (OU) process, on the fidelity of the 2-qubit Deutsch-Jozsa algorithm. We perform numerical simulations using Qiskit, systematically varying the noise strength ($\sigma_{\text{OU}}$) and correlation time ($\tau_c$) of the OU process. Our results demonstrate that the algorithm's fidelity exhibits a non-monotonic dependence on $\tau_c$, particularly at higher noise strengths, with certain intermediate correlation times proving more detrimental than others. We find that a standard Markovian dephasing model, matched to the single-step error variance of the OU process, accurately predicts fidelity only in the limit of very short correlation times. For longer correlation times, the Markovian approximation often overestimates the algorithm's fidelity, failing to capture the complex error dynamics introduced by the noise memory. These findings highlight the necessity of incorporating non-Markovian characteristics for accurate performance assessment of quantum algorithms on near-term devices and underscore the limitations of simpler, memoryless noise models.