Freiburg 2019 – scientific programme

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FM: Fall Meeting

FM 37: Open and Complex Quantum Systems II

FM 37.1: Talk

Tuesday, September 24, 2019, 14:00–14:15, 3042

Gauge optimization in locally purifying tensor network states — •Lennart Bittel¹, Albert H. Werner², and Martin Kliesch¹ — ¹Heinrich Heine University Düsseldorf, Germany — ²University of Copenhagen, Denmark

We have developed cost effective methods for finding good unitary gauges for locally purified tensor network quantum states. Tensor network methods have proven to be a useful tool to simulate interacting quantum systems. Such methods have also been extended from closed to open quantum systems. By relying on so-called local purifications positivity issues can be avoided and trace norm error control can be provided. However, purifications of quantum states have a unitary gauge freedom on the purifying system. This gauge freedom is shared by locally purified states and can practically lead to significant errors and large bond dimensions. In this work, we develop gauge optimization algorithms based on conjugate gradient methods and a version of adaptive linear regression. We demonstrate that this gauge optimization can be applied locally in order to significantly reduce the bond dimensions and to improve the accuracy of algorithms relying on local purifications with a small overhead.