Simulation of open quantum systems is an area of active research in quantum algorithms. In this Letter, we revisit the connection between Markovian open-system dynamics and averages of Hamiltonian real-time evolutions, which we refer to as Hamiltonian twirling channels. By applying the Lévy-Khintchine representation theorem, we clarify when and how dissipative dynamics can be realized using Hamiltonian twirling channels. Guided by the general theory, we explore Hamiltonian twirling with Gaussian, compound Poisson, and symmetric stable distributions and their algorithmic implications. These give Lindbladian families whose expected Hamiltonian simulation time ranges from $\mathrm{\Theta }(\sqrt{t})$ for Gaussian dephasing to $\mathrm{\Theta }(t)$ for compound-Poisson jumps, and $\mathrm{\Theta }(t^{1/\alpha })$ for symmetric $\alpha$-stable laws with $1<\alpha \le 2$. Moreover, we prove that these time complexities are asymptotically optimal for the classes studied here using an information-theoretic approach, establishing fundamental lower bounds on fast-forwarding quantum simulation algorithms for the first time to the best of our knowledge.

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• Open quantum systems
• Quantum algorithms & computation
• Quantum information theory
• Quantum simulation