Quantum trajectories for time-local non-Lindblad master equations

TL;DR

This paper introduces a pseudo-Lindblad quantum trajectory method for simulating non-Markovian open quantum systems, enabling efficient unraveling of dynamics beyond traditional Lindblad equations with minimal additional resources.

Contribution

The authors develop a novel pseudo-Lindblad quantum trajectory approach that handles non-Lindblad master equations without expanding the state space significantly.

Findings

Successfully applied to a single qubit system.

Effective for an interacting Fermi Hubbard chain.

Comparable computational effort to solving the full master equation.

Abstract

For the efficient simulation of open quantum systems we often use quantum jump trajectories given by pure states that evolve stochastically to unravel the dynamics of the underlying master equation. In the Markovian regime, when the dynamics is described by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation, this procedure is known as Monte-Carlo wavefunction (MCWF) approach . However, beyond ultraweak system-bath coupling, the dynamics of the system is not described by an equation of GKSL type, but rather by the Redfield equation, which can be brought into pseudo-Lindblad form. Here negative dissipation strengths prohibit the conventional approach. To overcome this problem, we propose a pseudo-Lindblad quantum trajectory (PLQT) unraveling. It does not require an effective extension of the state space, like other approaches, except for the addition of a single classical bit. We test the PLQT for the eternal non-Markovian master equation for a single qubit and an interacting Fermi Hubbard chain coupled to a thermal bath and discuss its computational effort compared to solving the full master equation.