{"arxiv_id":"quant-ph/9604038","incoming":{"papers":37,"sentences":54,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1901.08092","title":"Measurement-driven entanglement transition in hybrid quantum circuits","url":"/paper/1901.08092","section":"Introduction","sentence":"We thus will largely study “random Clifford circuits\" with the Haar unitaries replaced by random two-qubit Clifford unitaries, and the single qubit measurements restricted to the Pauli group [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"2003.12721","title":"Conformal invariance and quantum non-locality in critical hybrid circuits","url":"/paper/2003.12721","section":"Introduction","sentence":"The Gottesman-Knill theorem [ref] enables efficient simulation of Clifford circuits of up to thousands of qubits on a laptop, allowing us to perform detailed scaling analyses.","intent_p":0.97,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":2,"quotes":[{"arxiv_id":"0712.0103","title":"A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices","url":"/paper/0712.0103","section":"Asymptotic Coding Efficiency","sentence":"In [ref] , the quantum Hamming bound says that for an $[[n,k,d≥d=2t+1]]$ quantum code, [equation] and the asymptotic form is [equation] or [equation] The quantum singleton bound [ref] says that for an $[[n,k,d]]$ quantum code, [equation] or [equation] The Gilbert-Varshamov bound for a general quantum stabilizer codes, proved in Theorem 2 in [ref] , says that an $[[n,k,d=2t+1]]$ stabilizer code exists if [equation] or [equation] The Gilbert-Varshamov bound for CSS codes, proved in Section V in [ref] , says that an $[[n,k,d=2t+1]]$ CSS code exists if [equation] or [equation] The above known quantum bounds in the literature are depicted in Fig. [ref].","intent_p":0.97,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":24,"sentences":28,"quotes":[{"arxiv_id":"0712.0103","title":"A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices","url":"/paper/0712.0103","section":"Introduction","sentence":"The idea of stabilizer codes was proposed in [ref] and the properties of stabilizer codes were extensively addressed in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1607.01387","title":"Algebraic Methods for Quantum Codes on Lattices","url":"/paper/1607.01387","section":"Introduction","sentence":"Before long, a simple and systematic method of slicing the state vector space into discretely labeled subspaces with help of classical error correcting codes was discovered by Calderbank and Shor [ref] and Steane [ref] , and generalized to what is now known as stabilizer codes by Gottesman [ref] or symplectic/additive codes by Calderbank, Rains, Shor and Sloane [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2307.14602","title":"Supersymmetric conformal field theories from quantum stabilizer codes","url":"/paper/2307.14602","section":"Narain code CFTs","sentence":"An $[[n, k]]$ quantum stabilizer code $V_𝖲$ is defined as a $p^k$-dimensional subspace of $(^p)^n$ fixed by the stabilizer group $𝖲 = ⟨g_1, ⋯, g_n-k⟩$ generated by a commuting set of operators $g_i = g(^(i), ^(i)) (i=1, ⋯, n-k)$ [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"2402.11738","title":"Bulk and boundary entanglement transitions in the projective gauge-Higgs model","url":"/paper/2402.11738","section":"Introduction","sentence":"Some studies have focused on special classes of unitary gates, such as the Clifford gates or Majorana fermions, which can be efficiently simulated classically in combination with Pauli measurements due to the Gottesman-Knill theorem [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"2305.06365","title":"Lifting topological codes: Three-dimensional subsystem codes from two-dimensional anyon models","url":"/paper/2305.06365","section":"Intuition from the subsystem toric code","sentence":"Stabilizer [ref] and subsystem [ref] codes constitute two important and widely-studied classes of QEC codes.","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":22},"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/9604038","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T15:09:16+00:00","loaded_at":"2026-10-28T01:02:19.594640+00:00","evidence":"some","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"entries":[{"p":0.9,"quote":{"text":"Now, in order to associate an $n$-qubit state to any connected graph we follow the stabilizer formalism [ref] and to each vertex $v_i∈𝒱$ we associate an operator defined as","citing":"2404.02709","section":"Graph states"},"citing":[{"self":false,"year":2024,"title":"Certification of multi-qubit quantum systems with temporal inequalities","arxiv_id":"2404.02709"}],"verified":true,"paraphrase":"Followed this paper's stabilizer formalism to associate an n-qubit state to any connected graph."}],"papers_all":10,"self_papers":0,"self_entries":[]},{"kind":"comparison","label":"Compares with it","papers":1,"entries":[{"p":0.96,"quote":null,"citing":[{"self":false,"year":2007,"title":"A Construction of Quantum Stabilizer Codes Based on Syndrome Assignment by Classical Parity-Check Matrices","arxiv_id":"0712.0103"}],"verified":true,"paraphrase":"Constructed quantum stabilizer codes with parameters [[2^m, 2^m-m-2, 3]] that are the same as those constructed in this paper."}],"papers_all":2,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":2,"comparison":2,"method_or_tool":10},"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":8,"self_papers":2,"citing_papers":153,"sentences_read":9,"citing_sentences":218,"unambiguous_read":9,"typed_independent":14,"independent_papers":151,"by_kind_independent":{"extends":2,"comparison":2,"method_or_tool":10}},"input_sha256":"c8c688bd44e17900f8c7ec24be8dd8dd4656115942c43d51f43688507fe42840","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":"2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it."},"_links":{"html":"https://pith.science/paper/quant-ph/9604038"}}