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 $\lambda t \geq 1$, where $\lambda$ is the sum of the Hamiltonian coefficients and dissipative rates, the resulting approximation achieves normalized diamond-norm error at most $\varepsilon$ using $r=O(\lambda^2 t^2/\sqrt{\varepsilon})$ time slices, improving the $\varepsilon^{-1}$ 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 $\varepsilon^{-1/2}$ 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.

43 pages. The first two authors contributed equally

arXiv:2610.05288 [quant-ph]

(or arXiv:2610.05288v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.05288 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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