Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions

Quantum convolutional neural networks (QCNNs) are quantum circuits for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter systems in one dimension. Here we construct a QCNN that can perform phase recognition in two dimensions and correctly identify...

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Sander, Leon C, McMahon, Nathan A, Zapletal, Petr, Hartmann, Michael J
Format: Article
Language:English
Subjects:
Artificial neural networks
Condensed matter physics
Noise threshold
Phase transitions
Recognition
Topology
Online Access:Get full text
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Summary:Quantum convolutional neural networks (QCNNs) are quantum circuits for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter systems in one dimension. Here we construct a QCNN that can perform phase recognition in two dimensions and correctly identify the phase transition from a Toric Code phase with \(\mathbb{Z}_2\)-topological order to the paramagnetic phase. The network also exhibits a noise threshold up to which the topological order is recognized. Our work generalizes phase recognition with QCNNs to higher spatial dimensions and intrinsic topological order, where exploration and characterization via classical numerics become challenging.
ISSN:2331-8422