{"arxiv_id":"quant-ph/9608012","incoming":{"papers":59,"sentences":92,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0812.4682","title":"Topics in quantum information and the theory of open quantum systems","url":"/paper/0812.4682","section":"7.5 Summary and outlook","sentence":"It provides a natural means for extending key concepts such as the fidelity of a quantum channel [ref] or the entanglement fidelity [ref] to the case of subsystem codes.","intent_p":0.96,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":4,"quotes":[{"arxiv_id":"2009.07161","title":"Fault-tolerant Coding for Quantum Communication","url":"/paper/2009.07161","section":"Analyzing noisy quantum circuits","sentence":"In the following we will restrict to the concatenations [ref] of the $7$-qubit Steane code for which elementary gadgets have been constructed in [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"2412.20736","title":"Quantum communication and fault-tolerance","url":"/paper/2412.20736","section":"Fault-tolerance for quantum circuits","sentence":"The 7-qubit Steane code introduced in [ref] is an error correcting code that can correct all single-qubit errors, and that can be concatenated to improve protection against errors [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"2308.15437","title":"Existence of Pauli-like stabilizers for every quantum error-correcting code","url":"/paper/2308.15437","section":"Code parameters and codewords of a concatenated binary code","sentence":"We can then follow the standard procedure for finding the codewords and parameters of a concatenated code as in, e.g., Refs. [ref] : Replacing each $_in,C$-dimensional subsystem of the outer code by $_in$, the concatenated code hence has $_+ = (2^n_in)^q$ and $_+,C = 2^k_out$.","intent_p":0.8,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":4,"quotes":[{"arxiv_id":"1705.02174","title":"Long-range big quantum-data transmission","url":"/paper/1705.02174","section":"Introduction","sentence":"Comparison of approaches The main advantage of our scheme over existing ones [ref] is the superior scaling of the local resources with the distance, which is reduced from polynomial [ref] or polylogarithmic [ref] to constant.","intent_p":1.0,"contests_p":null},{"arxiv_id":"1605.09598","title":"On Quantum Tensor Product Codes","url":"/paper/1605.09598","section":"Introduction","sentence":"Compared with other quantum concatenation schemes, such as concatenated quantum codes (CQC) [ref] , the component code selections of QTPCs are more flexible than those of CQCs.","intent_p":0.94,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":34,"sentences":38,"quotes":[{"arxiv_id":"0901.1319","title":"Generalized Concatenated Quantum Codes","url":"/paper/0901.1319","section":"Introduction","sentence":"The idea of concatenated codes, originally described by Forney in a seminal book in 1966 [ref] , was introduced to quantum computation community three decades later [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2411.03683","title":"Polylog-time- and constant-space-overhead fault-tolerant quantum computation with quantum low-density parity-check codes","url":"/paper/2411.03683","section":"Concatenated Steane codes","sentence":"The concatenated Steane codes [ref] are constructed by recursively encoding each physical qubit of a Steane code into a logical qubit of the Steane code.","intent_p":0.86,"contests_p":null},{"arxiv_id":"2202.08084","title":"Entanglement-assisted concatenated quantum codes","url":"/paper/2202.08084","section":"Introduction","sentence":"Similarly in QECCs, the concatenated quantum codes (CQCs), introduced by Knill and Laflamme in 1996 [ref] , are also effective for constructing good quantum codes.","intent_p":0.83,"contests_p":null},{"arxiv_id":"2604.14931","title":"Learning to Concatenate Quantum Codes","url":"/paper/2604.14931","section":"Code Concatenation","sentence":"The underlying idea of code concatenation is to improve the logical error rate by recursively encoding the state into two or even multiple quantum error correction codes [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1604.05352","title":"Two dimensional quantum repeaters","url":"/paper/1604.05352","section":"Introduction","sentence":"High-rate quantum communication over long distances is possible using quantum repeaters, which either employ quantum error correction [ref] or create long-distance entanglement between two parties from shorter-distance entanglement via swapping and processing operations [ref] (see also [ref] ), thereby overcoming limitations due to noisy and lossy channels and limited local control.","intent_p":0.87,"contests_p":null}]}],"unlabelled_sentences":45},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"quant-ph/9608012","kind":"model","paper_version":1,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T21:37:11+00:00","loaded_at":"2026-10-28T01:04:13.368510+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"entries":[{"p":0.86,"quote":null,"citing":[{"self":false,"year":2020,"title":"Fault-tolerant Coding for Quantum Communication","arxiv_id":"2009.07161"}],"verified":true,"paraphrase":"Restricted its consideration to concatenations of this paper's kind, specifically of the 7-qubit Steane code with elementary gadgets constructed in another work."}],"papers_all":4,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":1,"comparison":2,"method_or_tool":4},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":15,"self_papers":1,"citing_papers":59,"sentences_read":19,"citing_sentences":93,"unambiguous_read":19,"typed_independent":7,"independent_papers":58,"by_kind_independent":{"extends":1,"comparison":2,"method_or_tool":4}},"input_sha256":"9304f1610d8d49bb362d0e481abfd2a2080d2a07ee22b17da5c023577801152c","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"1 later paper by other authors is listed below: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/quant-ph/9608012"}}