Quantum trajectory entanglement in various unravelings of Markovian dynamics
arxiv(2024)
Abstract
The cost of classical simulations of quantum many-body dynamics is often
determined by the amount of entanglement in the system. In this paper, we study
entanglement in stochastic quantum trajectory approaches that solve master
equations describing open quantum system dynamics. First, we introduce and
compare adaptive trajectory unravelings of master equations. Specifically,
building on Ref. [Phys. Rev. Lett. 128, 243601 (2022)], we study several greedy
algorithms that generate trajectories with a low average entanglement entropy.
Second, we consider various conventional unravelings of a one-dimensional open
random Brownian circuit and locate the transition points from area- to
volume-law-entangled trajectories. Third, we compare various trajectory
unravelings using matrix product states with a direct integration of the master
equation using matrix product operators. We provide concrete examples of
dynamics, for which the simulation cost of stochastic trajectories is
exponentially smaller than the one of matrix product operators.
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