Optimizing Tensor Network Contraction Using Reinforcement Learning

Eli Meirom, Haggai Maron, Shie Mannor, Gal Chechik
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:15278-15292, 2022.

Abstract

Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit requires computing the contraction of a large network of tensors. The order (path) of contraction can have a drastic effect on the computing cost, but finding an efficient order is a challenging combinatorial optimization problem. We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improvements over state-of-the-art techniques in three varieties of circuits, including the largest scale networks used in contemporary QC.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-meirom22a, title = {Optimizing Tensor Network Contraction Using Reinforcement Learning}, author = {Meirom, Eli and Maron, Haggai and Mannor, Shie and Chechik, Gal}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {15278--15292}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/meirom22a/meirom22a.pdf}, url = {https://proceedings.mlr.press/v162/meirom22a.html}, abstract = {Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit requires computing the contraction of a large network of tensors. The order (path) of contraction can have a drastic effect on the computing cost, but finding an efficient order is a challenging combinatorial optimization problem. We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improvements over state-of-the-art techniques in three varieties of circuits, including the largest scale networks used in contemporary QC.} }
Endnote
%0 Conference Paper %T Optimizing Tensor Network Contraction Using Reinforcement Learning %A Eli Meirom %A Haggai Maron %A Shie Mannor %A Gal Chechik %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-meirom22a %I PMLR %P 15278--15292 %U https://proceedings.mlr.press/v162/meirom22a.html %V 162 %X Quantum Computing (QC) stands to revolutionize computing, but is currently still limited. To develop and test quantum algorithms today, quantum circuits are often simulated on classical computers. Simulating a complex quantum circuit requires computing the contraction of a large network of tensors. The order (path) of contraction can have a drastic effect on the computing cost, but finding an efficient order is a challenging combinatorial optimization problem. We propose a Reinforcement Learning (RL) approach combined with Graph Neural Networks (GNN) to address the contraction ordering problem. The problem is extremely challenging due to the huge search space, the heavy-tailed reward distribution, and the challenging credit assignment. We show how a carefully implemented RL-agent that uses a GNN as the basic policy construct can address these challenges and obtain significant improvements over state-of-the-art techniques in three varieties of circuits, including the largest scale networks used in contemporary QC.
APA
Meirom, E., Maron, H., Mannor, S. & Chechik, G.. (2022). Optimizing Tensor Network Contraction Using Reinforcement Learning. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:15278-15292 Available from https://proceedings.mlr.press/v162/meirom22a.html.

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