Embedding of Tree Tensor Networks into Shallow Quantum Circuits

Shota Sugawara, Kazuki Inomata, Tsuyoshi Okubo, Synge Todo, Synge Todo, Synge Todo

2025

Abstract

Variational Quantum Algorithms (VQAs) are being highlighted as key quantum algorithms for demonstrating quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) devices, which are limited to executing shallow quantum circuits because of noise. However, the barren plateau problem, where the gradient of the loss function becomes exponentially small with system size, hinders this goal. Recent studies suggest that embedding tensor networks into quantum circuits and initializing the parameters can avoid the barren plateau. Yet, embedding tensor networks into quantum circuits is generally difficult, and methods have been limited to the simplest structure, Matrix Product States (MPSs). This study proposes a method to embed Tree Tensor Networks (TTNs), characterized by their hierarchical structure, into shallow quantum circuits. TTNs are suitable for representing two-dimensional systems and systems with long-range correlations, which MPSs are inadequate for representing. Our numerical results show that embedding TTNs provides better initial quantum circuits than MPS. Additionally, our method has a practical computational complexity, making it applicable to a wide range of TTNs. This study is expected to extend the application of VQAs to two-dimensional systems and those with long-range correlations, which have been challenging to utilize.

Paper Citation

in Harvard Style

Sugawara S., Inomata K., Okubo T. and Todo S. (2025). Embedding of Tree Tensor Networks into Shallow Quantum Circuits. In Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 1: QAIO; ISBN 978-989-758-737-5, SciTePress, pages 793-803. DOI: 10.5220/0013403200003890

in Bibtex Style

@conference{qaio25,
author={Shota Sugawara and Kazuki Inomata and Tsuyoshi Okubo and Synge Todo},
title={Embedding of Tree Tensor Networks into Shallow Quantum Circuits},
booktitle={Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 1: QAIO},
year={2025},
pages={793-803},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013403200003890},
isbn={978-989-758-737-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Agents and Artificial Intelligence - Volume 1: QAIO
TI - Embedding of Tree Tensor Networks into Shallow Quantum Circuits
SN - 978-989-758-737-5
AU - Sugawara S.
AU - Inomata K.
AU - Okubo T.
AU - Todo S.
PY - 2025
SP - 793
EP - 803
DO - 10.5220/0013403200003890
PB - SciTePress