Abstract
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. Furthermore, we implement these randomised algorithms using Classical Sampling (CS), demonstrating their gate complexity advantages over deterministic TS product formulas. This work systematically extends powerful randomisation techniques from Hamiltonian simulation to the general setting of Markovian open quantum systems, highlighting their potential to enable faster and more accurate simulations.