Physical Review A

Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise

Ronald F. Fox, I. R. Gatland, Rajarshi Roy, Gautam Vemuri

Published Dec 1, 1988• 409 citations

Abstract

The normal procedure for numerical simulation of exponentially correlated colored noise is superseded by the novel algorithm presented here. A differential algorithm is replaced by an integral algorithm which is faster, more accurate, and permits the use of longer step sizes.

DOI: 10.1103/physreva.38.5938

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Physical Review A

Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise

Ronald F. Fox, I. R. Gatland, Rajarshi Roy, Gautam Vemuri

Published Dec 1, 1988• 409 citations

Publisher

Abstract

DOI: 10.1103/physreva.38.5938

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O(n^3)

O(n^2)

for an

n

-qubit DD node with a single child node while keeping the

O(n^3)

run time in case of two distinct children nodes. We implement the algorithm as part of QolDDer, our Pauli-LIMDD simulator for quantum circuits, written from scratch in C/C++. The implementation realizes the theoretically-proven advantages of Pauli-LIMDDs on Clifford circuits, is significantly faster than the existing LIMDD simulators on such circuits, and on a public quantum-circuit data set often outperforms them by an order of magnitude. In the future, we envision that our work will enable further application and development of LIMDD variants, not only for quantum design tasks, but also for analysis of linear-algebra-based systems in general.

σ_{\text{OU}}

) and correlation time (

τ_c

) of the OU process. Our results demonstrate that the algorithm's fidelity exhibits a non-monotonic dependence on

τ_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.