{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T19:13:33Z","timestamp":1774120413062,"version":"3.50.1"},"reference-count":49,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:00:00Z","timestamp":1706054400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["1941583"],"award-info":[{"award-number":["1941583"]}]},{"name":"National Science Foundation","award":["1855879"],"award-info":[{"award-number":["1855879"]}]},{"name":"National Science Foundation","award":["2106189"],"award-info":[{"award-number":["2106189"]}]},{"name":"National Science Foundation","award":["2100013"],"award-info":[{"award-number":["2100013"]}]},{"name":"National Science Foundation","award":["2027844"],"award-info":[{"award-number":["2027844"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>Recent constructions of quantum low-density parity-check (QLDPC) codes provide optimal scaling of the number of logical qubits and the minimum distance in terms of the code length, thereby opening the door to fault-tolerant quantum systems with minimal resource overhead. However, the hardware path from nearest-neighbor-connection-based topological codes to long-range-interaction-demanding QLDPC codes is likely a challenging one. Given the practical difficulty in building a monolithic architecture for quantum systems, such as computers, based on optimal QLDPC codes, it is worth considering a distributed implementation of such codes over a network of interconnected medium-sized quantum processors. In such a setting, all syndrome measurements and logical operations must be performed through the use of high-fidelity shared entangled states between the processing nodes. Since probabilistic many-to-1 distillation schemes for purifying entanglement are inefficient, we investigate quantum error correction based entanglement purification in this work. Specifically, we employ QLDPC codes to distill GHZ states, as the resulting high-fidelity logical GHZ states can interact directly with the code used to perform distributed quantum computing (DQC), e.g. for fault-tolerant Steane syndrome extraction. This protocol is applicable beyond the application of DQC since entanglement distribution and purification is a quintessential task of any quantum network. We use the min-sum algorithm (MSA) based iterative decoder with a sequential schedule for distilling <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>3<\/mml:mn><\/mml:math>-qubit GHZ states using a rate <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0.118<\/mml:mn><\/mml:math> family of lifted product QLDPC codes and obtain an input fidelity threshold of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo>&amp;#x2248;<\/mml:mo><mml:mn>0.7974<\/mml:mn><\/mml:math> under i.i.d. single-qubit depolarizing noise. This represents the best threshold for a yield of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>0.118<\/mml:mn><\/mml:math> for any GHZ purification protocol. Our results apply to larger size GHZ states as well, where we extend our technical result about a measurement property of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mn>3<\/mml:mn><\/mml:math>-qubit GHZ states to construct a scalable GHZ purification protocol. <\/jats:p>","DOI":"10.22331\/q-2024-01-24-1233","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T16:33:16Z","timestamp":1706545996000},"page":"1233","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Entanglement Purification with Quantum LDPC Codes and Iterative Decoding"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2369-3159","authenticated-orcid":false,"given":"Narayanan","family":"Rengaswamy","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1024-8099","authenticated-orcid":false,"given":"Nithin","family":"Raveendran","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9022-3595","authenticated-orcid":false,"given":"Ankur","family":"Raina","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2365-4106","authenticated-orcid":false,"given":"Bane","family":"Vasi\u0107","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA"}]}],"member":"9598","published-online":{"date-parts":[[2024,1,24]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Matthew B Hastings, Jeongwan Haah, and Ryan O&apos;Donnell. 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