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Classical simulation of quantum many-body systems with a tree tensor network

Yaoyun Shi·Luming Duan·Guifre Vidal
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Abstract

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation} simulation algorithm for time evolution from a one dimensional lattice to a tree graph, while replacing a {\em matrix product state} with a {\em tree tensor network}. As an application, we show that any one-way quantum computation on a tree graph can be efficiently simulated with a classical computer.

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Yaoyun Shi, Luming Duan, Guifre Vidal. 2006-02-12. Classical simulation of quantum many-body systems with a tree tensor network. https://doi.org/10.1103/physreva.74.022320

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