[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124978-en":3,"doc-seo-124978-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},124978,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning","Error syndromes for heavy hexagonal codes and other topological codes such as surface code are commonly decoded with minimum weight perfect matching (MWPM). Recent work shows machine learning can decode topological codes efficiently using neural networks. This study proposes an ML-based decoder for heavy hexagonal code and evaluates threshold and pseudo-threshold under multiple noise models. It achieves ~5× higher threshold than MWPM. By introducing gauge equivalence for the subsystem setting, a linear-search method reduces error classes and improves threshold by ~14%, with a faster rank-based alternative.","arXiv :2210 .09730v2 [ cs .IT] 2 Apr 2024  \nEfficient Syndrome Decoder for Heavy Hexagonal QECC  \nvia Machine Learning  \nDebasmita Bhoumik 1,* , Ritajit Majumdar2 , Dhiraj Madan2 , Dhinakaran Vinayagamurthy2 , Shesha Raghunathan2 , and Susmita Sur-Kolay 1,+  \n1 Advanced Computing & Microelectronics Unit, Indian Statistical Institute, India  \n2 IBM Quantum, IBM India Research Lab  \n* [debasmita.ria21@gmail.com](debasmita.ria21@gmail.com)  \n+ [ssk@isical.ac.in](ssk@isical.ac.in)  \nAbstract  \nError syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold, for various noise models. We show that the proposed ML based decoding method achieves ∼ 5 × higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors, and thus a further improvement of ∼ 14% in the threshold over the basic ML decoder. Lastly, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.  \nIndex terms— QECC syndrome, topological code, subsystem code, heavy hexagonal code, gauge equivalence, neural networks  \n1 Introduction  \nQuantum computers excel over their classical counterparts [1, 2, 3, 4] for certain computational problems by attaining substantial speedup, due to the quantum mechanical properties of superposition and entanglement. But quantum states are highly fragile and a slightest unwanted rotation that may occur due to an interaction with the environment can introduce errors in the computation. An [[n, k, d]] quantum error correcting code (QECC) encodes k > 1 physical qubits into n > k physical qubits for correcting at most t = ⌊ ~~d ~~−2~~1~~ ⌋ errors. Some of the earlier QECCs [5, 6, 7] are however burdened with the Nearest Neighbour problem [8, 9] arising in the quantum hardware to realize a logical qubit. Two physical qubits i and j are said to be nearest neighbours if a 2-qubit operation involving (i, j) is feasible. An operation involving two non-neighbour physical qubits is costly since it requires multiple qubit swap operations, thereby reducing the computational speed and in turn making the system more error-prone. Topological QECCs [10, 11, 12, 13] resolve this problem by making the physical qubits for a logical qubit interact only with their neighbours.  \nRecently, industry research labs have been shifting towards the hexagonal architecture for their quantum computers. This architecture has the advantage of reducing the number of distinct frequencies, and thus crosstalk. The surface code [14] structure has been modified to a topological code with a heavy hexagonal structure [15] in order to become more suitable for these architectures. The heavy hexagonal code [15] uses a combination of degree-two and degree-three vertices in the topology, and can be considered as a hybrid of a surface code and a Bacon-Shor code [16] . This QECC reduces the distinct number of frequencies required in their realization by introducing more ancilla qubits (termed as flag qubits) for entanglement in the syndrome measurement [15] .  \nFor a distance d QECC, if more than ⌊ ~~d ~~−2~~1~~ ⌋ errors occur, then the QECC fails to correct those errors, leading to an incorrect logical state ","cbCaipn6wC1T8f0u","https://ap.wps.com/l/cbCaipn6wC1T8f0u","pdf",1671386,1,24,"English","en",105,"# Abstract\n# 1 Introduction\n## Quantum error correction and decoding goals\n## Heavy hexagonal code and hardware motivation\n## Threshold and pseudo-threshold\n## Related works and prior decoders","[{\"question\":\"How does the proposed ML-based decoder perform compared with the MWPM decoder for heavy hexagonal QECC?\",\"answer\":\"The ML-based approach achieves about 5× higher threshold values than the MWPM-based decoder under various noise models.\"},{\"question\":\"What is gauge equivalence in the context of heavy hexagonal subsystem codes?\",\"answer\":\"Gauge equivalence groups distinct errors into the same error class, allowing the decoder to search over fewer possibilities.\"},{\"question\":\"How is the number of error classes reduced and what improvement does it bring?\",\"answer\":\"A linear-search method determines equivalent error classes, giving a quadratic reduction for both bit flip and phase flip errors and improving the threshold by roughly 14% over the basic ML decoder.\"}]","Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning | 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does the proposed ML-based decoder perform compared with the MWPM decoder for heavy hexagonal QECC?","Question",{"text":75,"@type":76},"The ML-based approach achieves about 5× higher threshold values than the MWPM-based decoder under various noise models.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is gauge equivalence in the context of heavy hexagonal subsystem codes?",{"text":80,"@type":76},"Gauge equivalence groups distinct errors into the same error class, allowing the decoder to search over fewer possibilities.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the number of error classes reduced and what improvement does it bring?",{"text":84,"@type":76},"A linear-search method determines equivalent error classes, giving a quadratic reduction for both bit flip and phase flip errors and improving the threshold by roughly 14% over the basic ML 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