A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
- URL: http://arxiv.org/abs/2407.06594v1
- Date: Tue, 9 Jul 2024 06:55:19 GMT
- Title: A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
- Authors: Hongrui Chen, Bowen Li, Jianfeng Lu, Lexing Ying,
- Abstract summary: We study a qDRIFT-type randomized method to simulate the Lindblad equations.
For Lindblad dynamics generated by an ensemble of Lindbladians $mathcalL_a_a in mathcalA$, our approach implements a single randomly sampled Lindbladian $mathcalL_a$ at each time step.
- Score: 24.332332092371303
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study a qDRIFT-type randomized method to simulate the Lindblad equations. For Lindblad dynamics generated by an ensemble of Lindbladians $\{\mathcal{L}_a\}_{a \in \mathcal{A}}$, our approach implements a single randomly sampled Lindbladian $\mathcal{L}_a$ at each time step. The only assumption is that each $\mathcal{L}_a$ involves only a single jump operator with an efficient implementation available for the evolution $e^{t \mathcal{L}_a}$. A notable application of the randomized method is for quantum Gibbs sampling, where the Lindblad dynamics is utilized to prepare a specific Gibbs state. Unlike existing deterministic methods that require numerous jump operators to ensure ergodicity, our approach simplifies the implementation by using a single randomly sampled jump operator. As an example, we demonstrate that our method ensures fast thermalization of Hamiltonian systems characterized by random Pauli strings, where the spectral density closely adheres to the semi-circle law.
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