Dimension truncation for open quantum systems in terms of tensor networks

2018/01/23 by I. A. Luchnikov, Luchnikov, I. A., Stephen Vintskevich +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum many-body systems #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1801.07418

openalex publication_date 2018/01/23 · openalex created_date 2018/02/02 · openalex updated_date 2026/07/28

Abstract

We present novel and simple estimation of a minimal dimension required for an effective reservoir in open quantum systems. Using a tensor network formalism we introduce a new object called a reservoir network (RN). The reservoir network is the tensor network in the form of a Matrix Product State, which contains all effects of open dynamics. This object is especially useful for understanding memory effects. We discuss possible applications of the reservoir network and the estimation of dimension to develop new numerical and machine learning based methods for open quantum systems.

Citations

• TT-cross approximation for multidimensional arrays
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

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