[Seminar]Prof. Toshiya Hikihara "Efficacy of optimization of Network Structure in Tree-tensor network approaches"

Date

Location

C700/Zoom

Description

Speaker

Prof. Toshiya Hikihara / Gunma University

Title

Efficacy of optimization of Network Structure in Tree-tensor network approaches

Abstract

Tensor-network (TN) approaches have been applied to various problems in several fields, including quantum many-body physics, data science, and quantum information, and have achieved great success in recent years. TN is a contraction of low-rank tensors and is used to approximately represent a high-rank tensor, such as a wave function of a quantum many-body state. By introducing an upper limit to the dimension of the bonds in the TN, the computational cost is reduced from an exponential function to a polynomial of the number of qubits in the system. However, the upper limit on the bond dimension also induces a loss of accuracy. How to minimize the loss is an essential problem in TN approaches.

It has been recognized that the efficiency of TN in representing a state of interest strongly depends on the network structure. Therefore, finding the optimal network structure is a fundamental issue, though it is highly nontrivial and challenging. Recently, we have developed an algorithm to determine the optimal structure within the scope of the tree-tensor network (TTN), a TN without loops[1]. The algorithm realizes the structural optimization of TTN by iterating the local reconnection of tensors to make the network structure more suitable for representing the entanglements of the target quantum many-body state. We have demonstrated that the algorithm successfully obtains the optimal TTN structures for some toy models[1,2]. We have also examined the performance of the algorithm to enhance the accuracy of the calculation for quantum spin systems with a complex spatial structure[3]. In this talk, I will introduce the algorithm and present the numerical results for various quantum spin models to examine its efficiency. Possible applications of the algorithm to various problems, such as dynamics of quantum states, quantum chemistry, and machine learning, will also be discussed.

[1] TH, H. Ueda, K. Okunishi, K. Harada, T. Nishino, Phys. Rev. Research 5, 013031 (2023).
[2] TH, H. Ueda, K. Okunishi, K. Harada, T. Nishino, arXiv:2401.16000, accepted for the CCP2023 proceedings.
[3] TH, H. Ueda, K. Okunishi, K. Harada, T. Nishino, arXiv:2501.15514.

 

 

 

 

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