The manuscript excludes eight independent commuting Pauli generators of weight at most four for an [[11,3,3]] qubit stabilizer code, including degenerate and non-CSS codes. The published weight-five construction supplies the matching upper bound. The main PDF contains the cluster proof; the separate round-37 archive contains an alternative incidence-profile proof and its checker. This deposit identifies and preserves the manuscript reporting the result. It is an AI-assisted, unrefereed research manuscript. Archival publication does not establish novelty, external proof validation, or QIQC catalog acceptance. Archival version: 1.0. Manuscript date: 21 September 2026. The manuscript and source files are unchanged from the website snapshot taken on 25 September 2026. Background references are listed separately in the manuscript bibliography. Website: https://yuxuanzhang1995.github.io/agentic-research/lowweight-11-3-3/QIQC report: https://github.com/Naixu-Guo/quantum-open-problems/issues/110
The manuscript excludes eight independent commuting Pauli generators of weight at most four for an [[11,3,3]] qubit stabilizer code, including degenerate and non-CSS codes. The published weight-five construction supplies the matching upper bound. The main PDF contains the cluster proof; the separate round-37 archive contains an alternative incidence-profile proof and its checker. This deposit identifies and preserves the manuscript reporting the result. It is an AI-assisted, unrefereed research manuscript. Archival publication does not establish novelty, external proof validation, or QIQC catalog acceptance. Archival version: 1.0. Manuscript date: 21 September 2026. The manuscript and source files are unchanged from the website snapshot taken on 25 September 2026. Background references are listed separately in the manuscript bibliography. Website: https://yuxuanzhang1995.github.io/agentic-research/lowweight-11-3-3/QIQC report: https://github.com/Naixu-Guo/quantum-open-problems/issues/110
A versioned collection of twenty-one distinct AI-assisted research manuscripts on quantum information and quantum computation. Each manuscript is supplied as a separate PDF, identified by title, author, date, scope, website and QIQC report in README.md and MANUSCRIPTS.json. Sources for manuscripts 1–20 remain in sources-and-verification.zip; the new Chernoff manuscript's source and checking records are in chernoff-two-pass-source.zip. Collection version 1.3, 16 October 2026. This version adds Yuxuan Zhang, Two-pass local measurements beat the measured Chernoff exponent, manuscript version 1.0, 16 October 2026, 10 pages, file chernoff-two-pass.pdf. Theorem 1 gives faithful noncommuting four-dimensional states and a two-pass copywise LOCC counterexample to the universal equality in Eq. (4): the measured Chernoff exponent is below 0.677144, while the displayed protocol's exact exponent exceeds 0.68250256. The optimal unrestricted LOCC and SEP exponents, convergence of their optimal exponent sequences, and possible equality between the two classes remain unresolved. All twenty earlier manuscript PDFs and the earlier source archive are unchanged. Human and AI contributions. The author set the research directions, designed the harness that coordinated model tasks, tools, memory, and checking, supplied physical and mathematical intuitions and proof skeletons, and guided the development and revision of the research ideas. AI models developed detailed candidate arguments and derivations, searched the literature, wrote and ran computational checks, and drafted and revised the manuscripts under this supervision. This is an independently authored collection, not an official publication of the QIQC catalog. Archival publication does not establish novelty, external proof validation or catalog acceptance. Individual verification qualifications remain in each manuscript and index. Background references are distinguished from the manuscripts reporting the results. Withdrawn partial results and research logs are excluded. The eleven-qubit manuscript retains its individual DOI, 10.5281/zenodo.22968593. Prefer that individual DOI when citing that manuscript alone. Research website: https://yuxuanzhang1995.github.io/agentic-research/
ECEG V9: the submitted manuscript, editable LaTeX source and computational supplement. This repository deposit was created on 31 October 2026 to preserve a dated, DOI-identified copy. The manuscript and accompanying scientific files are unchanged from the Quantum Information Processing submission of 10 October 2026. This is a preprint, not an accepted or peer-reviewed publication. Full text and supplementary files are restricted; bibliographic metadata are public. AbstractQuantum records can encode different source observables while sharing the same reduced states and energy statistics. We determine the optimal fidelity for converting a family of such records using local diagonal controls on an arbitrary interaction hypergraph. The answer depends only on the branch overlap and the smallest unsupported interaction. A weighted phase inequality proves the optimum and supplies an attaining control. We also derive limits on shared access to records, distinguish equal endpoint marginals from stationary evolution, and extend the fidelity bound to mixed preparation errors and integrated control deviations. All results concern a specified finite-dimensional quantum model. FilesECEG_V9_QIP_Submitted.pdf: submitted English manuscript (18 pages).ECEG_V9_QIP_Source.zip: editable LaTeX source and template files.ESM_1.zip: numerical verification scripts, machine-readable results, reproducibility instructions and file manifest. The statement in the submitted manuscript that no public repository identifier was claimed describes the submission on 10 October 2026; the present DOI identifies this later archival deposit.
Manuscript submitted to Atoms (MDPI) on 30 September 2026 (manuscript atoms-4632260), with all code and data needed to reproduce its numerical results. Files: the manuscript (PDF, version 3.9), its LaTeX source with the ten figures (pauli_exclusion_wall_atoms_submission.zip), the supplementary material File S1 (pauli_exclusion_wall_supplementary.zip: the two-dimensional Q-ball scripts P1, P1b/P1c, P2 and P4 with their machine-readable outputs; the three-dimensional isorotating-cell analysis scripts and run reports, including the free-amplitude finite-element solver; the fully three-dimensional fixed-isospin pair relaxation; and the two-triad relaxation solver and reports, in phase to 3200 steps and out of phase to 4000 steps), and README.md, which describes the contents. The isorotating-cell technical note that the paper cites is a separate record, doi:10.5281/zenodo.23036586. This version completes the file set of the record first published on 30 September 2026, whose first version lacked the supplementary archive.
Low check weight is a crucial code property for fault-tolerant quantum computing, which underlies the strong interest in quantum low-density parity-check (qLDPC) codes. Here, we initiate the theory of weight-constrained stabilizer codes from various foundational perspectives including the complexity of computing code weight and the explicit boundary of feasible low-weight codes in both theoretical and practical settings. We first prove that computing the optimal generator weight of a stabilizer code is NP-hard, motivating efficiently computable bounds. We derive analytical lower bounds on check weight in terms of code rate and distance, identifying the minimum weights needed for single-qubit error detection and correction, as well as the sharp distance and rate limits of weight-three error-detecting codes. Matching constructions show that these bounds are tight in several regimes. To establish refined finite-size constraints, we develop a linear programming framework based on quantum weight enumerators subject to generator-weight constraints, yielding exact optimal weights for all parameter combinations with n≤9. Finally, we show that the same framework can incorporate architecture-dependent constraints, using the 127-qubit IBM Eagle chip as a concrete example. Our study brings the weight as a crucial parameter into coding theory and provides guidance for code design and utility in practical scenarios.
This research manuscript develops exact measurement-resource formulas for quantum erasure correction with stabilizer codes and an optimal sparse algorithm for selecting native surface-code checks. It studies known erasure locations, where the stabilizer observables may be chosen after the erased sites are identified. The central question is how many independent syndrome outcomes are necessary to distinguish Pauli errors on those sites, modulo stabilizers. For every prime-dimensional [[n,k,d]]_p stabilizer code encoding at least one logical qudit, the manuscript proves that the worst-case syndrome-resolving budget for δ erased sites is exactly 2δ whenever 0 ≤ δ < d. This includes degenerate codes. The result concerns the number of independent p-valued outcomes in the stated noiseless measurement model. The work is directly connected to the measurement-reduction setting studied by Ryutaroh Matsumoto in “Reducing measurements in quantum erasure correction by quantum local recovery,” Computational and Applied Mathematics, DOI: 10.1007/s40314-026-03881-4. It addresses the relationship between erasure-dependent measurement costs and code invariants, together with efficient selection of sufficient surface-code checks. The manuscript presents four connected results: Exact paired-column rank profile. For any matrix G over any field whose columns are partitioned into n labeled pairs, let r be its rank and ν the largest number of complete pairs whose columns are jointly independent. The maximum projected rank over all sets of δ pairs is exactly R(δ) = min{2δ, δ + ν, r}. A single ordering of the pairs realizes every maximum through its successive prefixes. The full profile therefore follows from two invariants, rather than requiring a separate optimization at every erasure size. Distance bounds and the exact worst-case syndrome budget. For an isotropic stabilizer space with k > 0, every inclusionwise maximal complete-pair independent set A satisfies d ≤ |A| + 1. Consequently, ν ≥ d − 1, yielding the exact 2δ worst-case budget below distance. The argument also gives a constructive extension property: every independent-pair set smaller than d − 1 can be enlarged by adding another pair. Particular correctable erasure patterns can require fewer outcomes because of stabilizers supported inside the erased region. Checkable CSS certificates. For Calderbank–Shor–Steane codes, complete-pair independence becomes simultaneous column independence in the X-check and Z-check matrices. Classical matroid intersection supplies an exact rank-partition certificate for ν. A matching independent set and partition provide lower and upper certificates that can be verified using finite-field elimination. Optimal native surface-code check selection. For binary check matrices with at most two nonzero entries per column, the restricted matrix is represented by a sparse graph with boundary pins. Connected components determine a minimum-cardinality native check basis in O(v_I + e_I) time. A pinned component retains every check; an unpinned component omits one check. With nonnegative additive costs, omitting a most expensive check in each unpinned component also minimizes total cost. The two CSS check systems are processed independently. The accompanying verification uses exact arithmetic over GF(2), GF(3), and GF(5). The algebra audit covers 120 general paired matrices and 12,276 subset-rank evaluations, including exact distance checks for 137 positive-logical-dimension code instances and 401 maximal-set distance checks. The graph audit covers 1,785 exhaustive sparse column multisets, 5,355 matrix/cost combinations, 500 additional seeded instances, and named boundary regressions. Both audit programs passed again during preparation of the release. These finite checks support implementation correctness; the general mathematical statements are supported by the supplied proofs. The release includes the complete manuscript, editable LaTeX source, Python native-check selector, exact audit programs, recorded results, generator data, figures, reproduction instructions, and an explicit claim-status record. The selector and audits require only Python 3.10 or later and its standard library; matplotlib is needed only to regenerate the figure. The results apply to independent syndrome information and classical check selection. They do not establish bounds for arbitrary coherent recovery, noisy fault-tolerant extraction, physical circuit depth, or one fixed measurement schedule that must serve every erasure pattern. At or above distance, the general formula remains an algebraic rank profile rather than a universal recovery guarantee. Classical matroid parity, matroid intersection, and incidence-rank methods are acknowledged foundations; historical priority for the presented combination is not certified. Ōrynthéa ∿ Qhuil is relevant to research on quantum error correction, erasure decoding, stabilizer and CSS codes, surface codes, quantum local recovery, measurement complexity, and matroid optimization. This mathematical research under the author designation Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
Quantum low-density parity-check (qLDPC) codes can be implemented by measuring only low-weight checks, making them compatible with noisy quantum hardware and central to the quest to build noise-resilient quantum computers. A fundamental open question is how constraints on check weight limit the achievable parameters of qLDPC codes. Here, we study stabilizer and subsystem codes with constrained check weight, combining analytical arguments with numerical optimization to establish strong upper bounds on their parameters. We show that stabilizer codes with checks of weight at most three cannot have nontrivial distance. We also prove tight tradeoffs between rate and distance for broad families of CSS stabilizer and subsystem codes with checks of weight at most four and two, respectively. Notably, our bounds are applicable to general qLDPC codes, as they rely only on check-weight constraints without assuming geometric locality or special graph connectivity. In the finite-size regime, we derive numerical upper bounds using linear programming techniques and identify explicit code constructions that approach these limits, delineating the landscape of practically relevant qLDPC codes with tens or hundreds of physical qubits.