Ancilla-Free Fast-Forwarding Lindbladian Simulation Algorithms by Hamiltonian Twirling

• URL: http://arxiv.org/abs/2511.10253v1
• Date: Fri, 14 Nov 2025 01:41:42 GMT
• Title: Ancilla-Free Fast-Forwarding Lindbladian Simulation Algorithms by Hamiltonian Twirling
• Authors: Minbo Gao, Zhengfeng Ji, Chenghua Liu,
• Abstract summary: We show that the time-$t$ evolution map can be expressed exactly a Gaussian twirl over the unitary orbit $mathrme-mathrmi Hs_sinmathbbR$.<n>This structural insight allows us to design a fast-forwarding algorithm for Lindbladian simulation.
• Score: 2.8802622551493773
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulation of open quantum systems is an area of active research in quantum algorithms. In this work, we revisit the connection between Markovian open-system dynamics and averages of Hamiltonian real-time evolutions, which we refer to as Hamiltonian twirling channels. Focusing on the class of Lindbladians with a single Hermitian jump operator $H$ recently studied in Shang et al. (arXiv:2510.06759), we show that the time-$t$ evolution map can be expressed exactly a Gaussian twirl over the unitary orbit ${\{\mathrm{e}^{-\mathrm{i} Hs}\}}_{s\in\mathbb{R}}$. This structural insight allows us to design a fast-forwarding algorithm for Lindbladian simulation that achieves diamond-norm error $\varepsilon$ with time complexity $O\big(\sqrt{t\log(1/\varepsilon)}\big)$ -- matching the performance of Shang et al. while requiring no auxiliary registers or controlled operations. The resulting ancilla-free and control-free algorithm is therefore more amenable to near-term experimental implementation. By purifying the Gaussian twirl procedure and performing a conjugate measurement, we derive a continuous-variable quantum phase estimation algorithm. In addition, by applying the Lévy-Khintchine representation theorem, we clarify when and how a dissipative dynamics can be realized using Hamiltonian twirling channels. Guided by the general theory, we explore Hamiltonian twirling with compound Poisson distributions and their potential algorithmic implications.

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