The Augmented Tree Tensor Network Cookbook

TL;DR

This paper introduces the augmented tree tensor network (aTTN), a tensor network ansatz enhanced with disentanglers, enabling efficient simulation of higher-dimensional quantum lattice systems and providing an open-source implementation with benchmarking results.

Contribution

It presents a detailed implementation and benchmarking of aTTNs for simulating large 2D quantum lattice models, demonstrating advantages over other tensor network methods.

Findings

aTTNs effectively simulate large 2D lattices up to 32x32 spins.

Benchmarking shows aTTNs outperform matrix product states and standard TTNs in accuracy for given computational costs.

Open-source implementation available within the Quantum TEA library.

Abstract

An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable for simulating higher-dimensional lattices, where the entanglement increases with the lattice size even for states that obey the area law. These lecture notes serve as a detailed guide for implementing the aTTN algorithms. We present a variational algorithm for ground state search and discuss the measurement of observables, and offer an open-source implementation within the Quantum TEA library. We benchmark the performance of the ground state search for different parameters and hyperparameters in the square lattice quantum Ising model and the triangular lattice Heisenberg model for up to $32 \times 32$ spins. The benchmarks identify the regimes where the aTTNs offer advantages in accuracy relative to computational cost compared to matrix product states and tree tensor networks.