Tensor network methods with graph enhancement

TL;DR

This paper extends tensor network algorithms with graph enhancement techniques, improving the description of ground and time-evolved states in quantum many-body systems, especially for complex graph states.

Contribution

It introduces the RAGE algorithm applied to tensor tree states and PEPS, enhancing their ability to model complex quantum states and dynamics.

Findings

Graph enhancement improves ground state descriptions.

Weighted graph states enhance tensor network accuracy.

Method extends classical simulability of quantum states.

Abstract

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)] to other tensor-network states such as the tensor tree states (TTS) and projected entangled pair states (PEPS). We investigate the suitability of the bare TTS to describe ground states, showing that the description of certain graph states and condensed matter models improves. We investigate graph-enhanced tensor-network states, demonstrating that in some cases (disturbed graph states and for certain quantum circuits) the combination of weighted graph states with tensor tree states can greatly improve the accuracy of the description of ground states and time evolved states. We comment on delineating the boundary of the classically efficiently simulatable states of quantum many-body systems.