Optimization of Reordering Procedures in HOTRG for Distributed Parallel Computing

Yamada, Haruka; Imakura, Akira; Imamura, Toshiyuki; Sakurai, Tetsuya

doi:10.1109/ipdpsw.2018.00150

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Our work differs from theirs in that we focus on approximate PEPS algorithms with polynomial time complexity, which allows for larger bond dimensions with a controlled error and consequently serves different application needs. A related algorithm, the higher-order tensor renormalization group (HOTRG) has also been studied in a distributed parallel setting [62], where an optimal reordering procedure for tensor contractions used in HOTRG is proposed. In comparison, our work provides a more general approach via the use of Cyclops, which automates the performance optimization within tensor contractions.…”

Section: Related Workmentioning

confidence: 99%

Efficient 2D Tensor Network Simulation of Quantum Systems

Pang

Hao

Dugad

et al. 2020

SC20: International Conference for High Performance Computing, Networking, Storage and Analysis

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Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States (PEPS) are well-suited for key classes of physical systems and quantum circuits. However, direct contraction of PEPS networks has exponential cost, while approximate algorithms require computations with large tensors. We propose new scalable algorithms and software abstractions for PEPS-based methods, accelerating the bottleneck operation of contraction and refactorization of a tensor subnetwork. We employ randomized SVD with an implicit matrix to reduce cost and memory footprint asymptotically. Further, we develop a distributed-memory PEPS library and study accuracy and efficiency of alternative algorithms for PEPS contraction and evolution on the Stampede2 supercomputer. We also simulate a popular near-term quantum algorithm, the Variational Quantum Eigensolver (VQE), and benchmark Imaginary Time Evolution (ITE), which compute ground states of Hamiltonians.

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Section: Related Workmentioning

confidence: 99%

Efficient 2D Tensor Network Simulation of Quantum Systems

Pang

Hao

Dugad

et al. 2020

SC20: International Conference for High Performance Computing, Networking, Storage and Analysis

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“…A way of implementation of this method is not unique. A comclete example is shown in [12]. On one hand, the HOTRG has the above-mentioned merit, but on the other hand, computational cost and memory space requirement of it in higher-dimensional simple lattice model are far from cheap.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Computing Method for the Higher Order Tensor Renormalization Group

Yamashita,

Sakurai

2021

Preprint

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In this paper, we propose a parallel computing method for the Higher Order Tensor Renormalization Group (HOTRG) applied to a d-dimensional (d ≥ 2) simple lattice model. Sequential computation of the HOTRG requires O(χ 4d−1 ) computational cost, where χ is bond dimension, in a step to contract indices of tensors. When we simply distribute elements of a local tensor to each process in parallel computing of the HOTRG, frequent communication between processes occurs. The simplest way to avoid such communication is to hold all the tensor elements in each process, however, it requires O(χ 2d ) memory space. In the presented method, placement of a local tensor element to more than one process is accepted and sufficient local tensor elements are distributed to each process to avoid communication between processes during considering computation step. For the bottleneck part of computational cost, such distribution is achieved by distributing elements of two local tensors to χ 2 processes according to one of the indices of each local tensor which are not contracted during considering computation. In the case of d ≥ 3, computational cost in each process is reduced to O(χ 4d−3 ) and memory space requirement in each process is kept to be O(χ 2d−1 ).

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A parallel computing method for the higher order tensor renormalization group

Yamashita

Sakurai

2022

Computer Physics Communications

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Optimization of Reordering Procedures in HOTRG for Distributed Parallel Computing

Cited by 4 publications

References 12 publications

Efficient 2D Tensor Network Simulation of Quantum Systems

Efficient 2D Tensor Network Simulation of Quantum Systems

A Parallel Computing Method for the Higher Order Tensor Renormalization Group

A parallel computing method for the higher order tensor renormalization group

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