Tensor-Network-Based Unraveling of Non-Markovian Dynamics in Large Spin Chains via the Influence Martingale Approach

Abstract

Classical simulation of open quantum system dynamics remains challenging due to the exponential growth of the Hilbert space, the need to accurately capture dissipation and decoherence, and the added complexity of memory effects in the non-Markovian regime. We develop an efficient algorithm for simulating both Markovian and non-Markovian dynamics in large one-dimensional quantum systems. Extending the Tensor Jump Method, which combines TDVP-based tensor-network evolution with a Suzuki--Trotter decomposition of stochastic trajectories, our approach incorporates time-dependent decay rates--treating positive rates as time-inhomogeneous Markovian processes and negative rates via the Influence Martingale formalism to unravel time-local non-Markovian dynamics. We further introduce the concept of the `influence radius' to achieve a resource-efficient framework enabling scalable simulations of open-system dynamics in the non-Markovian regime, as demonstrated for a one-dimensional transverse-field Ising chain comprising up to 100 spin qubits.