Tatiana Vovk (University of Innsbruck) - Minimising entanglement in tensor-network trajectories*

*Full title: Minimising entanglement in tensor-network quantum trajectories
Abstract:
In this seminar we introduce a way to directly leverage noise in trajectory-based stochastic methods to simulate open quantum many-body systems. Our key proposition, as outlined in Ref. [1], revolves around the insight that the same system dynamics can be obtained by different stochastic propagators, which give distinct ensembles of pure-state trajectories. Specifically, we introduce an adaptive optimisation strategy for selecting the stochastic propagator, with the objective of minimising the entanglement, which serves as a proxy of the expected cost of classically representing various trajectories. The physical mechanism underlying this idea is reminiscent of the phenomenon of measurement-induced phase transitions [2]. We complement our discussion with explicit examples of one-dimensional open quantum dynamics, demonstrating that optimised trajectory-based methods employing matrix product states (MPSs) can yield an exponential reduction in classical computational cost compared to other MPS-trajectory-based methods or compared to conventional matrix product density operator technique. We also note that our findings are interesting not only from a computational point of view, but also from a fundamental quantum-information-theoretic perspective, since they give rise to heuristic algorithms for finding upper bounds on mixed-state entanglement measures, such as the entanglement of formation, a task that holds an independent and intrinsic interest [3].
[1] Vovk, T., Pichler, H. Phys. Rev. Lett 128, 24 (2022).
[2] Skinner, B., Ruhman, J., and Nahum, A. Phys. Rev. X 9, 3 (2019).
[3] Uhlmann, A. Entropy 12, 7 (2010).
Date of talk: 2023-12-01