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We introduce a prototype FPGA decoder implementing the recently discovered Relay-BP algorithm and targeting memory experiments on the $[[144,12,12]]$ bivariate bicycle quantum low-density parity check code.
“Windowed Decoding of Protograph-Based LDPC Convolutional Codes Over Erasure Channels”
Aravind. Iyengar et al · 2011
Earlier work this paper cites.
“Simplified variable-scaled min sum LDPC decoder for irregular LDPC codes”
Ahmed. Emran and Maha Elsabrouty · 2014
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“Quantum error correction for quantum memories”
Barbara. Terhal · 2015
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“NISQ+: Boosting quantum computing power by approximating quantum error correction”
Adam Holmes et al · 2020
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“Stim: a fast stabilizer circuit simulator”
Craig Gidney · 2021
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“Syndrome-Based Min-Sum vs OSD-0 Decoders: FPGA Implementation and Analysis for Quantum LDPC Codes”
Javier Valls, Francisco Garcia-Herrero, Nithin Raveendran and Bane Vasić · 2021
Earlier work this paper cites.
“AFS: Accurate, Fast, and Scalable Error-Decoding for Fault-Tolerant Quantum Computers”
Poulami Das et al · 2022
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“Parallel window decoding enables scalable fault tolerant quantum computation”
Luka Skoric et al · 2022
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“High-threshold and low-overhead fault-tolerant quantum memory”
Sergey Bravyi et al · 2023
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“WIT-Greedy: Hardware System Design of Weighted ITerative Greedy Decoder for Surface Code”
Wang Liao et al · 2023
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“Learning high-accuracy error decoding for quantum processors”
Johannes Bausch et al · 2024
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“Demonstrating real-time and low-latency quantum error correction with superconducting qubits”, 2024
Laura Caune et al · 2024
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“FPGA-Based Distributed Union-Find Decoder for Surface Codes”
Namitha Liyanage, Yue Wu, Siona Tagare and Lin Zhong · 2024
Cited alongside, same era.
“Local Clustering Decoder: a fast and adaptive hardware decoder for the surface code”, 2024
“IBM Quantum Roadmap”, 2025
IBM · 2025
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“A 22-nm Surface Code Decoder Using Greedy Algorithm”
Junichiro Kadomoto, Ren Aoyama and Kazutoshi Kobayashi · 2025
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“Decoding Correlated Errors in Quantum LDPC Codes”
Arshpreet Maan, Francisco-Garcia Herrero, Alexandru Paler and Valentin Savin · 2025
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“Improved belief propagation is sufficient for real-time decoding of quantum memory”, 2025
Tristan Müller et al · 2025
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“Decision-tree decoders for general quantum LDPC codes”, 2025
Kai. Ott, Bence Hetényi and Michael. Beverland · 2025
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“Micro Blossom: Accelerated Minimum-Weight Perfect Matching Decoding for Quantum Error Correction”
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Abbas. Ziad et al · 2024
Cited alongside, same era.
“A real-time, scalable, fast and resource-efficient decoder for a quantum computer”
Ben Barber et al · 2025
Cited alongside, same era.
“Exploring the FPGA and ASIC design space of belief propagation and ordered statistics decoders for Quantum Error Correction Codes”
Daniel Bascones, Francisco Garcia-Herrero and Javier Valls
Cited in the paper.
Yue Wu, Namitha Liyanage and Lin Zhong · 2025
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“Tour de gross: A modular quantum computer based on bivariate bicycle codes”
Theodore Yoder et al · 2025
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