Abstract
Non-Markovian effects are important in modeling the behavior of open quantum systems arising in solid-state physics, quantum optics as well as in study of biological and chemical systems. The non-Markovian environment is often approximated by discrete bosonic modes, thus mapping it to a Lindbladian or Hamiltonian simulation problem. While systematic constructions of such modes have been previously proposed, the resulting approximation lacks rigorous and general convergence guarantees. In this Letter, we show that under some physically motivated assumptions on the system-environment interaction, the finite-time dynamics of the non-Markovian open quantum system computed with a sufficiently large number of modes is guaranteed to converge to the true result. Furthermore, we show that this approximation error typically falls off polynomially with the number of modes. Our results lend rigor to classical and quantum algorithms for approximating non-Markovian dynamics.
Highlights
Quantum systems invariably interact with their environment, and any simulation technique used to model their behavior needs to capture this interaction. Such interactions are analyzed within the Markovian approximation, wherein the system dynamics is described by the Lindbladian master equation [1]
A number of quantum systems arising in solid-state physics [2,3,4,5], quantum optics [6,7,8,9,10], as well as quantum biology and chemistry [11,12,13,14] cannot be modeled accurately within the Markovian approximation and the non-Markovian nature of the environment needs to be explicitly taken into account
The second method is to use star-to-chain transformation [33,34], which uses the Lanczos iteration to identify a 1D chain of discrete bosonic modes with nearest neighbor couplings that approximate the environment and map the problem of computing non-Markovian quantum dynamics to a Hamiltonian simulation problem
Summary
Quantum systems invariably interact with their environment, and any simulation technique used to model their behavior needs to capture this interaction. Simulating non-Markovian open quantum systems is difficult since it is usually not possible to formulate a dynamical equation for the system state from a given physical model of the system-environment interaction.
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