{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T00:08:40Z","timestamp":1768608520435,"version":"3.49.0"},"reference-count":43,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T00:00:00Z","timestamp":1768521600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council","award":["114-2221-E-007-066-MY3"],"award-info":[{"award-number":["114-2221-E-007-066-MY3"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Recent research has shown that syndrome-based belief propagation using layered scheduling (sLBP) can not only accelerate the convergence rate but also improve the error rate performance by breaking the quantum trapping sets for quantum low-density parity-check (QLDPC) codes, showcasing a result distinct from classical error correction codes. In this paper, we consider edge-wise informed dynamic scheduling (IDS) for QLDPC codes based on syndrome-based residual belief propagation (sRBP). However, the construction of QLDPC codes and the identical prior intrinsic information assignment will result in an equal residual in many edges, causing a performance limitation for sRBP. Two heuristic strategies, including edge pool design and error pre-correction, are introduced to tackle this obstacle and quantum trapping sets. Then, a novel sRBP equipped with a predict-and-reduce-error mechanism (PRE-sRBP) is proposed, which can provide over one order of performance gain on the considered bicycle codes and symmetric hypergraph (HP) code under similar iterations compared to sLBP.<\/jats:p>","DOI":"10.22331\/q-2026-01-16-1967","type":"journal-article","created":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T13:36:51Z","timestamp":1768570611000},"page":"1967","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Informed Dynamic Scheduling for QLDPC Codes"],"prefix":"10.22331","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3549-0073","authenticated-orcid":false,"given":"Tzu-Hsuan","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3438-0385","authenticated-orcid":false,"given":"Yeong-Luh","family":"Ueng","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering & Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan"}]}],"member":"9598","published-online":{"date-parts":[[2026,1,16]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Nikolas P. Breuckmann and Jens Niklas Eberhardt. ``Quantum low-density parity-check codes''. PRX Quantum 2, 040101 (2021).","DOI":"10.1103\/PRXQuantum.2.040101"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Maxime A. Tremblay, Nicolas Delfosse, and Michael E. Beverland. ``Constant-overhead quantum error correction with thin planar connectivity''. Phys. Rev. Lett. 129, 050504 (2022).","DOI":"10.1103\/PhysRevLett.129.050504"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Sergey Bravyi, Andrew W. Cross, Dmitri Maslov Jay M. Gambetta, Patrick Rall, and Theodore J. Yoder. ``High-threshold and low-overhead fault-tolerant quantum memory''. Nature 627, 778 (2024).","DOI":"10.1038\/s41586-024-07107-7"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Michael A. Nielsen and Isaac L. Chuang. ``Quantum computation and quantum information''. Cambridge University Press. (2009). 10th Anniversary edition.","DOI":"10.1017\/cbo9780511976667"},{"key":"4","doi-asserted-by":"publisher","unstructured":"A.R. Calderbank, E.M. Rains, P.M. Shor, and N.J.A. Sloane. ``Quantum error correction via codes over GF(4)''. IEEE Transactions on Information Theory 44, 1369 (1998).","DOI":"10.1109\/18.681315"},{"key":"5","doi-asserted-by":"publisher","unstructured":"D.J.C. MacKay, G. Mitchison, and P.L. McFadden. ``Sparse-graph codes for quantum error correction''. IEEE Transactions on Information Theory 50, 2315\u20132330 (2004).","DOI":"10.1109\/TIT.2004.834737"},{"key":"6","doi-asserted-by":"publisher","unstructured":"David Poulin and Yeojin Chung. ``On the iterative decoding of sparse quantum codes''. Quant. Inf. Comput. 8, 0987\u20131000 (2008).","DOI":"10.26421\/QIC8.10-8"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Nithin Raveendran and Bane Vasi\u0107. ``Trapping sets of quantum LDPC codes''. Quantum 5 (2021).","DOI":"10.22331\/q-2021-10-14-562"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Pavel Panteleev and Gleb Kalachev. ``Degenerate quantum LDPC codes with good finite length performance''. Quantum 5, 585 (2021).","DOI":"10.22331\/q-2021-11-22-585"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Joschka Roffe, David R. White, Simon Burton, and Earl Campbell. ``Decoding across the quantum low-density parity-check code landscape''. Phys. Rev. Res. 2, 043423 (2020).","DOI":"10.1103\/PhysRevResearch.2.043423"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Javier Valls, Francisco Garcia-Herrero, Nithin Raveendran, and Bane Vasi\u0107. ``Syndrome-based min-sum vs OSD-0 decoders: FPGA implementation and analysis for quantum ldpc codes''. IEEE Access 9, 138734\u2013138743 (2021).","DOI":"10.1109\/ACCESS.2021.3118544"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Andres I. Vila Casado, Miguel Griot, and Richard Wesel. ``Improving LDPC decoders via informed dynamic scheduling''. In Information Theory Workshop. Pages 208\u2013213. (2007).","DOI":"10.1109\/ITW.2007.4313075"},{"key":"12","unstructured":"Gal Elidan, Ian McGraw, and Daphne Koller. ``Residual belief propagation: Informed scheduling for asynchronous message passing'' (2012). arXiv:1206.6837."},{"key":"13","doi-asserted-by":"publisher","unstructured":"A. I. V. Casado, M. Griot, and R. D. Wesel. ``Informed dynamic scheduling for belief-propagation decoding of LDPC codes''. In 2007 IEEE International Conference on Communications. Pages 932\u2013937. (2007).","DOI":"10.1109\/ICC.2007.158"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Andres I. Vila Casado, Miguel Griot, and Richard D. Wesel. ``LDPC decoders with informed dynamic scheduling''. IEEE Transactions on Communications 58, 3470\u20133479 (2010).","DOI":"10.1109\/TCOMM.2010.101910.070303"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Tofar C.-Y. Chang, Pin-Han Wang, Jian-Jia Weng, I-Hsiang Lee, and Yu T. Su. ``Belief-propagation decoding of LDPC codes with variable node\u2013centric dynamic schedules''. IEEE Transactions on Communications 69, 5014\u20135027 (2021).","DOI":"10.1109\/TCOMM.2021.3078776"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Jean-Pierre Tillich and Gilles Z\u00e9mor. ``Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength''. IEEE Transactions on Information Theory 60, 1193\u20131202 (2014).","DOI":"10.1109\/TIT.2013.2292061"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Daniel Eric Gottesman. ``Stabilizer codes and quantum error correction''. PhD thesis. California Institute of Technology. (1997).","DOI":"10.7907\/rzr7-dt72"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Richard Cleve. ``Quantum stabilizer codes and classical linear codes''. Phys. Rev. A 55, 4054\u20134059 (1997).","DOI":"10.1103\/PhysRevA.55.4054"},{"key":"19","doi-asserted-by":"publisher","unstructured":"A. R. Calderbank and Peter W. Shor. ``Good quantum error-correcting codes exist''. Phys. Rev. A 54, 1098\u20131105 (1996).","DOI":"10.1103\/PhysRevA.54.1098"},{"key":"20","doi-asserted-by":"publisher","unstructured":"A. M. Steane. ``Error correcting codes in quantum theory''. Phys. Rev. Lett. 77, 793\u2013797 (1996).","DOI":"10.1103\/PhysRevLett.77.793"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Emanuel Knill and Raymond Laflamme. ``Theory of quantum error-correcting codes''. Phys. Rev. A 55, 900\u2013911 (1997).","DOI":"10.1103\/PhysRevA.55.900"},{"key":"22","doi-asserted-by":"publisher","unstructured":"F.R. Kschischang, B.J. Frey, and H.-A. Loeliger. ``Factor graphs and the sum-product algorithm''. IEEE Transactions on Information Theory 47, 498\u2013519 (2001).","DOI":"10.1109\/18.910572"},{"key":"23","unstructured":"D. J. C. MacKay. ``Information theory, inference and learning algorithms''. Cambridge University Press. (2003)."},{"key":"24","doi-asserted-by":"publisher","unstructured":"Ching-Yi Lai and Kao-Yueh Kuo. ``Log-domain decoding of quantum LDPC codes over binary finite fields''. IEEE Transactions on Quantum Engineering 2, 1\u201315 (2021).","DOI":"10.1109\/TQE.2021.3113936"},{"key":"25","unstructured":"Tom Richardson. ``Error floors of LDPC codes''. Proc. annual Allerton conference on commun. control and computing (2003)."},{"key":"26","doi-asserted-by":"publisher","unstructured":"D.E. Hocevar. ``A reduced complexity decoder architecture via layered decoding of LDPC codes''. In IEEE Workshop onSignal Processing Systems, 2004. SIPS 2004. Pages 107\u2013112. (2004).","DOI":"10.1109\/SIPS.2004.1363033"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Juntan Zhang and M.P.C. Fossorier. ``Shuffled iterative decoding''. IEEE Transactions on Communications 53, 209\u2013213 (2005).","DOI":"10.1109\/TCOMM.2004.841982"},{"key":"28","doi-asserted-by":"publisher","unstructured":"J. Chen and M.P.C. Fossorier. ``Density evolution for two improved BP-based decoding algorithms of LDPC codes''. IEEE Communications Letters 6, 208\u2013210 (2002).","DOI":"10.1109\/4234.1001666"},{"key":"29","unstructured":"3GPP. ``5G; NR; multiplexing and channel coding (release 15) 38.212''. document Technical specification (TS) (2018)."},{"key":"30","doi-asserted-by":"publisher","unstructured":"Xingcheng Liu, Zhenzhu Zhou, Ru Cui, and Erwu Liu. ``Informed decoding algorithms of LDPC codes based on dynamic selection strategy''. IEEE Transactions on Communications 64, 1357\u20131366 (2016).","DOI":"10.1109\/TCOMM.2016.2527642"},{"key":"31","doi-asserted-by":"publisher","unstructured":"Xingcheng Liu, Chunlei Fan, and Xuechen Chen. ``Dynamic scheduling decoding of LDPC codes based on Tabu search''. IEEE Transactions on Communications 65, 4612\u20134621 (2017).","DOI":"10.1109\/TCOMM.2017.2732950"},{"key":"32","doi-asserted-by":"publisher","unstructured":"Xingcheng Liu, Li'e Zi, Dong Yang, and Zhongfeng Wang. ``Improved decoding algorithms of LDPC codes based on reliability metrics of variable nodes''. IEEE Access (2019).","DOI":"10.1109\/ACCESS.2019.2904173"},{"key":"33","doi-asserted-by":"publisher","unstructured":"R. Gallager. ``Low-density parity-check codes''. IRE Transactions on Information Theory 8, 21\u201328 (1962).","DOI":"10.1109\/TIT.1962.1057683"},{"key":"34","unstructured":"Tzu-Hsuan Huang. ``PRE-sRBP''. https:\/\/github.com\/quantumrbp\/srbp.git (2026)."},{"key":"35","doi-asserted-by":"publisher","unstructured":"Nedeljko Varnica, Marc P. C. Fossorier, and Aleksandar Kavcic. ``Augmented belief propagation decoding of low-density parity check codes''. IEEE Transactions on Communications 55, 1308\u20131317 (2007).","DOI":"10.1109\/TCOMM.2007.900611"},{"key":"36","doi-asserted-by":"publisher","unstructured":"D. Chase. ``Class of algorithms for decoding block codes with channel measurement information''. IEEE Transactions on Information Theory 18, 170\u2013182 (1972).","DOI":"10.1109\/TIT.1972.1054746"},{"key":"37","unstructured":"Joschka Roffe. ``LDPC: Python tools for low density parity check codes''. https:\/\/pypi.org\/project\/ldpc\/ (2022)."},{"key":"38","doi-asserted-by":"publisher","unstructured":"Tzu-Hsuan Huang and Yeong-Luh Ueng. ``A binary BP decoding using posterior adjustment for quantum LDPC codes''. In ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Pages 9001\u20139005. (2024).","DOI":"10.1109\/ICASSP48485.2024.10446153"},{"key":"39","doi-asserted-by":"crossref","unstructured":"H. Yao, W. A. Laban, C. Hager, A. G. i Amat, and H. D. Pfister. ``Belief propagation decoding of quantum LDPC codes with guided decimation'' (2023). arXiv:2312.10950.","DOI":"10.1109\/ISIT57864.2024.10619083"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Julien Du Crest, Francisco Garcia-Herrero, Mehdi Mhalla, Valentin Savin, and Javier Valls. ``Layered decoding of quantum ldpc codes''. In 2023 12th International Symposium on Topics in Coding (ISTC). Pages 1\u20135. (2023).","DOI":"10.1109\/ISTC57237.2023.10273477"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Adam Holmes, Mohammad Reza Jokar, Ghasem Pasandi, Yongshan Ding, Massoud Pedram, and Frederic T. Chong. ``Nisq+: Boosting quantum computing power by approximating quantum error correction''. In 2020 ACM\/IEEE 47th Annual International Symposium on Computer Architecture (ISCA). Pages 556\u2013569. (2020).","DOI":"10.1109\/ISCA45697.2020.00053"},{"key":"42","doi-asserted-by":"publisher","unstructured":"Kao-Yueh Kuo and Ching-Yi Lai. ``Refined belief propagation decoding of sparse-graph quantum codes''. IEEE Journal on Selected Areas in Information Theory 1, 487\u2013498 (2020).","DOI":"10.1109\/JSAIT.2020.3011758"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-01-16-1967\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T13:37:31Z","timestamp":1768570651000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-01-16-1967\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,16]]},"references-count":43,"URL":"https:\/\/doi.org\/10.22331\/q-2026-01-16-1967","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,16]]},"article-number":"1967"}}