An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code
Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a clas...
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MDPI AG
2025-06-01
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| Series: | Entropy |
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| author | Yuan-Hang Zhang Zhian Jia Yu-Chun Wu Guang-Can Guo |
| author_facet | Yuan-Hang Zhang Zhian Jia Yu-Chun Wu Guang-Can Guo |
| author_sort | Yuan-Hang Zhang |
| collection | DOAJ |
| description | Restricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a class of highly entangled quantum states that are central to quantum error correction. Given a set of stabilizer generators, we develop an efficient algorithm to determine both the RBM architecture and the exact values of its parameters. Our findings provide new insights into the expressive power of RBMs, highlighting their capability to encode highly entangled states, and may serve as a useful tool for the classical simulation of quantum error-correcting codes. |
| format | Article |
| id | doaj-art-4a54fdadb5a044ae890f0593abb44a74 |
| institution | OA Journals |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-4a54fdadb5a044ae890f0593abb44a742025-08-20T02:21:06ZengMDPI AGEntropy1099-43002025-06-0127662710.3390/e27060627An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer CodeYuan-Hang Zhang0Zhian Jia1Yu-Chun Wu2Guang-Can Guo3Department of Physics, University of California, San Diego, CA 92093, USACentre for Quantum Technologies, National University of Singapore, Singapore 117543, SingaporeCAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, ChinaCAS Key Laboratory of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, ChinaRestricted Boltzmann machines (RBMs) have demonstrated considerable success as variational quantum states; however, their representational power remains incompletely understood. In this work, we present an analytical proof that RBMs can exactly and efficiently represent stabilizer code states—a class of highly entangled quantum states that are central to quantum error correction. Given a set of stabilizer generators, we develop an efficient algorithm to determine both the RBM architecture and the exact values of its parameters. Our findings provide new insights into the expressive power of RBMs, highlighting their capability to encode highly entangled states, and may serve as a useful tool for the classical simulation of quantum error-correcting codes.https://www.mdpi.com/1099-4300/27/6/627neural network quantum statequantum stabilizer coderestricted Boltzmann machine |
| spellingShingle | Yuan-Hang Zhang Zhian Jia Yu-Chun Wu Guang-Can Guo An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code Entropy neural network quantum state quantum stabilizer code restricted Boltzmann machine |
| title | An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code |
| title_full | An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code |
| title_fullStr | An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code |
| title_full_unstemmed | An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code |
| title_short | An Efficient Algorithmic Way to Construct Boltzmann Machine Representations for Arbitrary Stabilizer Code |
| title_sort | efficient algorithmic way to construct boltzmann machine representations for arbitrary stabilizer code |
| topic | neural network quantum state quantum stabilizer code restricted Boltzmann machine |
| url | https://www.mdpi.com/1099-4300/27/6/627 |
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