Fast Random Compilers for Time-Dependent and Time-Independent Lindbladian Simulation
Abstract
Randomized product formulas provide simple and flexible methods for quantum simulation. While qDRIFT-type randomized simulation has been extended to Lindbladian dynamics, higher-order randomized compilers have primarily been developed for Hamiltonian simulation. In this work, we develop first- and second-order randomized sampling algorithms for Lindbladian simulation in both the time-independent and time-dependent settings. Building on first-order qDRIFT-type Lindbladian simulation, we introduce a qSWIFT-type second-order correction for time-independent Lindbladians with a finite local decomposition. For λt ≥ 1, where λ is the sum of the Hamiltonian coefficients and dissipative rates, the resulting approximation achieves normalized diamond-norm error at most ε using r=O(λ2 t2/√ε) time slices, improving the ε−1 precision dependence of the first-order qDRIFT-type approximation. We then develop first- and second-order continuous-time sampling algorithms for general time-dependent Lindbladians, with the second-order construction likewise achieving an ε−1/2 dependence on the target precision in the number of time slices. We further extend the time-dependent construction to a linear-combination input model over local Hamiltonian and dissipative generators, allowing the randomized sampler to be formulated in terms of local evolutions rather than the full time-dependent Lindbladian. Because the second-order corrected maps need not be CPTP, we use them to estimate observable expectation values rather than to deterministically prepare output states.
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BibTeX
@misc{seo2026fast,
title = {{Fast Random Compilers for Time-Dependent and Time-Independent Lindbladian Simulation}},
author = {Youngjin Seo and Dhrumil Patel and Hyukjoon Kwon and Mark M. Wilde},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05288},
eprint = {2610.05288},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05288},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fast Random Compilers for Time-Dependent and Time-Independent Lindbladian Simulation
AU - Youngjin Seo
AU - Dhrumil Patel
AU - Hyukjoon Kwon
AU - Mark M. Wilde
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05288
UR - https://arxiv.org/abs/2610.05288
AB - Randomized product formulas provide simple and flexible methods for quantum simulation. While qDRIFT-type randomized simulation has been extended to Lindbladian dynamics, higher-order randomized compilers have primarily been developed for Hamiltonian simulation. In this work, we develop first- and second-order randomized sampling algorithms for Lindbladian simulation in both the time-independent and time-dependent settings. Building on first-order qDRIFT-type Lindbladian simulation, we introduce a qSWIFT-type second-order correction for time-independent Lindbladians with a finite local decomposition. For λt ≥ 1, where λ is the sum of the Hamiltonian coefficients and dissipative rates, the resulting approximation achieves normalized diamond-norm error at most ε using r=O(λ^2 t^2/√ε) time slices, improving the ε^−1 precision dependence of the first-order qDRIFT-type approximation. We then develop first- and second-order continuous-time sampling algorithms for general time-dependent Lindbladians, with the second-order construction likewise achieving an ε^−1/2 dependence on the target precision in the number of time slices. We further extend the time-dependent construction to a linear-combination input model over local Hamiltonian and dissipative generators, allowing the randomized sampler to be formulated in terms of local evolutions rather than the full time-dependent Lindbladian. Because the second-order corrected maps need not be CPTP, we use them to estimate observable expectation values rather than to deterministically prepare output states.
ER -