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Agentic Proofs for QIQC: Collected Manuscripts

Yuxuan Zhang

Published Sep 26, 2026• 0 citations
Publisher

Abstract

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 Withdrawn partial results and research logs are excluded.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/

DOI
10.5281/zenodo.22969545

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The optimal check weight of an [[11,3,3]] stabilizer code is five

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An infinite family of non-star trees admitting Laplacian peak state transfer

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Unrefereed AI-assisted preprint, version 0.2.2, 9 October 2026. No author affiliation is given. For each m >= 1, set q = m^2 + m + 1. Attach q intermediate vertices to a root and q - 1 leaves to each intermediate vertex. This produces infinitely many pairwise nonisomorphic non-star trees of order q^2 + 1, with root Laplacian spectral support {0, m^2 + 1, (m + 1)^2 + 1}. The symbolic argument establishes Laplacian peak state transfer at time pi from the root to an intermediate vertex for odd m and to a leaf for even m, addressing Open Problem 7.1 of Coutinho, Guo and Schmeits, arXiv:2505.11986v4. The ten-vertex m = 1 member is their known Figure 10 example. Phase alignment is an application of their Lemma 5.2 and Corollary 5.3; the general peak-time classification follows their Theorem 5.4 and Corollary 5.5. The contribution presented here is the explicit infinite family and its spectral coefficients, targets and gcd calculation. For the specified pairs, all positive peak times are odd multiples of pi/g, where g = 5 when m = 2 mod 5 and otherwise g = 1. Novelty and priority are not certified. Peak transfer means attaining the mutual-projector absolute-sum bound, not unit amplitude. The probabilities tend to zero along both parity subsequences. This does not establish perfect transfer, efficient long-distance quantum communication or a classification of all trees. Exact standard-library reruns check actual full-tree Laplacians for m = 1..5, quotients for m = 1..1000, and gcd/phase regressions for m = 1..10000. Those finite checks support, not replace, the symbolic all-parameter proof and the analytic all-real-time Bezout argument. No complete Lean or other proof-assistant verification is supplied. 本研究は、清水竣平が個人の自主研究として企画・進行した、AIを活用した数学探索です。清水は探索方針の指示、検証の手配、成果の取りまとめを担当しました。証明の構成、計算による検証、原稿作成の大部分にはAIを使用しています。検証方法とその範囲は本文に記載しており、人間の専門家による査読は未実施です。 This work is an AI-assisted mathematical exploration initiated and coordinated by Shunpei Shimizu as a personal independent research project. Shimizu directed the exploration, arranged verification, and compiled the results. AI systems performed most proof construction, computational checking, and manuscript preparation. The verification methods and their scope are documented in the manuscript. The work has not received specialist human peer review. The submitter has not independently certified every mathematical step. Separate AI analyses and implementations are not human refereeing. No cited-author or institutional endorsement is implied. Read peak_trees_en_v0.2.2.tex first. The current package is Quantum_peak_trees_publication_v0.2.2_20261009.zip; QUANTUM_TREES_README_PUBLICATION_v0.2.2_EN.md explains its contents. Version 0.2.2 removes author affiliation; mathematical text, equations, statements, proofs and verification programs are unchanged from version 0.2.1. The current package omits old manuscript sources and old full ZIPs. Earlier verification records retain their original dates; they are not human peer review. The built-in LaTeX compiler failed at Windows environment setup before TeX diagnostics. No PDF has been generated or visually verified; editable TeX and exact-check code are supplied. Documentation clarification, 10 October 2026. The retained README_EN.txt and README_JA.md are historical documentation; the corresponding preserved v0.1.0 copies describe the 8 October 2026 working draft. QUANTUM_TREES_README_PUBLICATION_v0.2.1_EN.md describes the superseded v0.2.1 package. Their source names, payload inventories, draft-status statements and no-Publish instructions are dated history, not the current record state or operative instructions. Independent checks in those documents mean separate AI analyses or implementations, not human refereeing. The current entrypoints are peak_trees_en_v0.2.2.tex, Quantum_peak_trees_publication_v0.2.2_20261009.zip and QUANTUM_TREES_README_PUBLICATION_v0.2.2_EN.md. Refer to the current TeX for the argument where historical checker comments mention an absent review.md. This notice makes no change to the mathematical manuscript or verification programs. Publication packaging clarification, 10 October 2026. In addition to the three historical READMEs identified above, the two QUANTUM_TREES_ATTRIBUTION_AI_ROLE_ADDENDUM files and novelty_attribution_math_monitor_review_20261009.zip are dated supplementary review records. The r1 addendum and the current v0.2.2 manuscript give the operative author and AI contribution disclosure. The novelty archive also compares other manuscripts; those comparisons are context, not additional results of this Quantum record. Earlier private-save and no-publication instructions describe past workflow only. Current scientific claims are the explicitly stated tree-family construction and specified-pair peak times. No mathematical content, verification program or frozen historical attachment is changed by this clarification.

•Oct 10, 2026•0 citations

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We construct an effective carrier model within the Worldline–Residue–Resource–Action framework. Two conditionally independent registers encode prime-factor multiplicities. A label-symmetric equality projector controls a common source coupled to two supplied particle-pair channels. One pulse generates the earlier collision-statistic probabilities without address-dependent interaction strength. A restricted single-register obstruction and a classification of diagonal permutation-invariant effects specify the construction’s resource assumptions. The implementation reproduces species probabilities, but not the preceding interface’s coherent output channel. Bare-energy conservation holds at the calibrated reference volume; detuning away from resonance requires interaction energy and switching work. A response identity relates the reference pressure-volume moment to the logarithmic-volume derivative of mean pulse work. Composition with the implemented muon-decay kernel recovers energy and pressure histories at full conversion. This is an executable effective interaction candidate and compatibility analysis; lepton identities, weak interactions, and the full fifteen-channel carrier are not derived from arithmetic alone. Version 0.2, editorial revision of 9 October 2026. Includes the English manuscript, Korean guide, and reproducibility archive. The 123 carrier-level checks are internal consistency checks, not experimental validation or external journal peer review. The manuscript was prepared before this deposit; its preparation-time statement that no public DOI had been assigned is superseded by this record. Preceding WRRA records: r11, https://doi.org/10.5281/zenodo.23237629; particle interface v0.2, https://doi.org/10.5281/zenodo.23241511; dynamic decays v0.2, https://doi.org/10.5281/zenodo.23246308. Correction release 0.2-r1 (9 October 2026): Table 3 now states that the hot electron branch has a positive pressure-volume moment; the antielectron-neutrino overbar in Section 6.2 is correctly rendered in the PDF. The scientific model, reproduction code and numerical results are unchanged. The manuscript retains its v0.2 designation and filenames; 0.2-r1 identifies this corrected deposit. A third Astra medium AI internal review and post-correction check examined the final files. Both required corrections were resolved, with no further mandatory technical corrections identified. The review report is included. This is not external journal peer review or acceptance. Earlier statements in the guide/review about two review rounds describe the historical pre-correction state.

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Quantum Proofs

Thomas Vidick, John Watrous

Quantum Proofs provides an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, it discusses non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.

now publishers, Inc. eBooks•Jan 1, 2016•22 citations
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/
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
This compendium presents a structured collection of computational problems with credible prospects for realizing meaningful quantum advantage, focused on describing problem characteristics rather than specific algorithms. It is intended for non-quantum researchers and practitioners with strong computational backgrounds, particularly domain experts, seeking to assess the relevance of quantum methods to real-world problems. The compendium focuses on enumerating core problems for which there is good evidence that a quantum computer can realize more than a quadratic speedup in offline non-relativized time-complexity (e.g., as opposed to in oracular settings, streaming models, or communication advantages). Entries characterize the structural constraints that real-world instances must satisfy to realize those advantages in practice. The intention is to provide a reference that can be leveraged to connect quantum algorithms to practical use cases.
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.
Unrefereed AI-assisted preprint, version 0.2.2, 9 October 2026. No author affiliation is given. For each m >= 1, set q = m^2 + m + 1. Attach q intermediate vertices to a root and q - 1 leaves to each intermediate vertex. This produces infinitely many pairwise nonisomorphic non-star trees of order q^2 + 1, with root Laplacian spectral support {0, m^2 + 1, (m + 1)^2 + 1}. The symbolic argument establishes Laplacian peak state transfer at time pi from the root to an intermediate vertex for odd m and to a leaf for even m, addressing Open Problem 7.1 of Coutinho, Guo and Schmeits, arXiv:2505.11986v4. The ten-vertex m = 1 member is their known Figure 10 example. Phase alignment is an application of their Lemma 5.2 and Corollary 5.3; the general peak-time classification follows their Theorem 5.4 and Corollary 5.5. The contribution presented here is the explicit infinite family and its spectral coefficients, targets and gcd calculation. For the specified pairs, all positive peak times are odd multiples of pi/g, where g = 5 when m = 2 mod 5 and otherwise g = 1. Novelty and priority are not certified. Peak transfer means attaining the mutual-projector absolute-sum bound, not unit amplitude. The probabilities tend to zero along both parity subsequences. This does not establish perfect transfer, efficient long-distance quantum communication or a classification of all trees. Exact standard-library reruns check actual full-tree Laplacians for m = 1..5, quotients for m = 1..1000, and gcd/phase regressions for m = 1..10000. Those finite checks support, not replace, the symbolic all-parameter proof and the analytic all-real-time Bezout argument. No complete Lean or other proof-assistant verification is supplied. 本研究は、清水竣平が個人の自主研究として企画・進行した、AIを活用した数学探索です。清水は探索方針の指示、検証の手配、成果の取りまとめを担当しました。証明の構成、計算による検証、原稿作成の大部分にはAIを使用しています。検証方法とその範囲は本文に記載しており、人間の専門家による査読は未実施です。 This work is an AI-assisted mathematical exploration initiated and coordinated by Shunpei Shimizu as a personal independent research project. Shimizu directed the exploration, arranged verification, and compiled the results. AI systems performed most proof construction, computational checking, and manuscript preparation. The verification methods and their scope are documented in the manuscript. The work has not received specialist human peer review. The submitter has not independently certified every mathematical step. Separate AI analyses and implementations are not human refereeing. No cited-author or institutional endorsement is implied. Read peak_trees_en_v0.2.2.tex first. The current package is Quantum_peak_trees_publication_v0.2.2_20261009.zip; QUANTUM_TREES_README_PUBLICATION_v0.2.2_EN.md explains its contents. Version 0.2.2 removes author affiliation; mathematical text, equations, statements, proofs and verification programs are unchanged from version 0.2.1. The current package omits old manuscript sources and old full ZIPs. Earlier verification records retain their original dates; they are not human peer review. The built-in LaTeX compiler failed at Windows environment setup before TeX diagnostics. No PDF has been generated or visually verified; editable TeX and exact-check code are supplied. Documentation clarification, 10 October 2026. The retained README_EN.txt and README_JA.md are historical documentation; the corresponding preserved v0.1.0 copies describe the 8 October 2026 working draft. QUANTUM_TREES_README_PUBLICATION_v0.2.1_EN.md describes the superseded v0.2.1 package. Their source names, payload inventories, draft-status statements and no-Publish instructions are dated history, not the current record state or operative instructions. Independent checks in those documents mean separate AI analyses or implementations, not human refereeing. The current entrypoints are peak_trees_en_v0.2.2.tex, Quantum_peak_trees_publication_v0.2.2_20261009.zip and QUANTUM_TREES_README_PUBLICATION_v0.2.2_EN.md. Refer to the current TeX for the argument where historical checker comments mention an absent review.md. This notice makes no change to the mathematical manuscript or verification programs. Publication packaging clarification, 10 October 2026. In addition to the three historical READMEs identified above, the two QUANTUM_TREES_ATTRIBUTION_AI_ROLE_ADDENDUM files and novelty_attribution_math_monitor_review_20261009.zip are dated supplementary review records. The r1 addendum and the current v0.2.2 manuscript give the operative author and AI contribution disclosure. The novelty archive also compares other manuscripts; those comparisons are context, not additional results of this Quantum record. Earlier private-save and no-publication instructions describe past workflow only. Current scientific claims are the explicitly stated tree-family construction and specified-pair peak times. No mathematical content, verification program or frozen historical attachment is changed by this clarification.
We construct an effective carrier model within the Worldline–Residue–Resource–Action framework. Two conditionally independent registers encode prime-factor multiplicities. A label-symmetric equality projector controls a common source coupled to two supplied particle-pair channels. One pulse generates the earlier collision-statistic probabilities without address-dependent interaction strength. A restricted single-register obstruction and a classification of diagonal permutation-invariant effects specify the construction’s resource assumptions. The implementation reproduces species probabilities, but not the preceding interface’s coherent output channel. Bare-energy conservation holds at the calibrated reference volume; detuning away from resonance requires interaction energy and switching work. A response identity relates the reference pressure-volume moment to the logarithmic-volume derivative of mean pulse work. Composition with the implemented muon-decay kernel recovers energy and pressure histories at full conversion. This is an executable effective interaction candidate and compatibility analysis; lepton identities, weak interactions, and the full fifteen-channel carrier are not derived from arithmetic alone. Version 0.2, editorial revision of 9 October 2026. Includes the English manuscript, Korean guide, and reproducibility archive. The 123 carrier-level checks are internal consistency checks, not experimental validation or external journal peer review. The manuscript was prepared before this deposit; its preparation-time statement that no public DOI had been assigned is superseded by this record. Preceding WRRA records: r11, https://doi.org/10.5281/zenodo.23237629; particle interface v0.2, https://doi.org/10.5281/zenodo.23241511; dynamic decays v0.2, https://doi.org/10.5281/zenodo.23246308. Correction release 0.2-r1 (9 October 2026): Table 3 now states that the hot electron branch has a positive pressure-volume moment; the antielectron-neutrino overbar in Section 6.2 is correctly rendered in the PDF. The scientific model, reproduction code and numerical results are unchanged. The manuscript retains its v0.2 designation and filenames; 0.2-r1 identifies this corrected deposit. A third Astra medium AI internal review and post-correction check examined the final files. Both required corrections were resolved, with no further mandatory technical corrections identified. The review report is included. This is not external journal peer review or acceptance. Earlier statements in the guide/review about two review rounds describe the historical pre-correction state.
Quantum Proofs provides an overview of many of the known results concerning quantum proofs, computational models based on this concept, and properties of the complexity classes they define. In particular, it discusses non-interactive proofs and the complexity class QMA, single-prover quantum interactive proof systems and the complexity class QIP, statistical zero-knowledge quantum interactive proof systems and the complexity class QSZK, and multiprover interactive proof systems and the complexity classes QMIP, QMIP*, and MIP*. Quantum Proofs is mainly intended for non-specialists having a basic background in complexity theory and quantum information. A typical reader may be a student or researcher in either area desiring to learn about the fundamentals of the (actively developing) theory of quantum interactive proofs.