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arXiv · 2503.08626

Tensor networks for quantum computing

Aleksandr Berezutskii·Minzhao Liu·Atithi Acharya·Roman Ellerbrock·Johnnie Gray·Reza Haghshenas·Zichang He·Abid Khan·Viacheslav Kuzmin·Dmitry Lyakh·Danylo Lykov·Salvatore Mandrà·Christopher Mansell·Alexey Melnikov·Artem Melnikov·Vladimir Mironov·Dmitry Morozov·Florian Neukart·Alberto Nocera·Michael A. Perlin·Michael Perelshtein·Matthew Steinberg·Ruslan Shaydulin·Benjamin Villalonga·Markus Pflitsch·Marco Pistoia·Valerii Vinokur·Yuri Alexeev
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Abstract

In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities and the challenges of the tensor-network techniques.

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Aleksandr Berezutskii, Minzhao Liu, Atithi Acharya, Roman Ellerbrock, Johnnie Gray, Reza Haghshenas, Zichang He, Abid Khan, Viacheslav Kuzmin, Dmitry Lyakh, Danylo Lykov, Salvatore Mandrà, Christopher Mansell, Alexey Melnikov, Artem Melnikov, Vladimir Mironov, Dmitry Morozov, Florian Neukart, Alberto Nocera, Michael A. Perlin, Michael Perelshtein, Matthew Steinberg, Ruslan Shaydulin, Benjamin Villalonga, Markus Pflitsch, Marco Pistoia, Valerii Vinokur, Yuri Alexeev. 2025-03-11. Tensor networks for quantum computing. https://doi.org/10.1038/s42254-025-00853-1

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