Automatic structural optimization of tree tensor networks

Abstract

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in improving its approximation accuracy. In this paper, we propose a TTN algorithm that enables us to automatically optimize the network structure by local reconnections of isometries to suppress the bipartite entanglement entropy on their legs. The algorithm can be seamlessly implemented to such a conventional TTN approach as density-matrix renormalization group. We apply the algorithm to the inhomogeneous antiferromagnetic Heisenberg spin chain having a hierarchical spatial distribution of the interactions. We then demonstrate that the entanglement structure embedded in the ground-state of the system can be efficiently visualized as a perfect binary tree in the optimized TTN. Possible improvements and applications of the algorithm are also discussed.

12 pages, 11 figures, 2 tables, v2: accepted version, to appear in Phys. Rev. Research

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• Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Differentiable matrix product states for simulating variational quantum computational chemistry
• The State Preparation of Multivariate Normal Distributions using Tree Tensor Network
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• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Improving accuracy of tree-tensor network approach by optimization of network structure
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states
• Explaining Anomalies with Tensor Networks
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Holographic Aspects of Dynamical Mean-Field Theory
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• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Hierarchical Search of Tree Tensor Networks for High-Dimensional Data
• Optimization of Quantum Systems Emulation via a Variant of the Bandwidth Minimization Problem