[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86088-en":3,"doc-seo-86088-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},86088,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","p-Form Gauge Dynamics and Digital Quantum Simulation Flux and Cosmological Constant Neutralization","A Hamiltonian framework is developed for Zk p-form gauge fields on arbitrary oriented cell complexes in any dimension, defining gauge qudits on p-cells, charged boundary qudits on (p−1)-cells, Gauss-law generators via ∂p, and magnetic checks via ∂p+1. The cellular structure yields local dressed Wilson operators and, at k=2, a Calderbank–Shor–Steane check complex for quantum error correction. For p=2,k=2, magnetic 3-cell terms vanish and one-form Gauss-law constraints are solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables and reduced dynamics map to an Ising-type plaquette model; cap–tube quenches and exact diagonalization quantify flux-discharge relaxation and a finite-size dynamical crossover related to top-form discharge and cosmological-constant neutralization.","arXiv :2607 . 10950v1 [ quant-ph] 12 Jul 2026  \np-Form Gauge Dynamics and Digital Quantum Simulation – Flux and Cosmological Constant Neutralization –  \nSoo-Jong Rey  \nKwangwoon University  \nSeoul, Korea  \n[sjrey@kw. ac. kr](sjrey@kw. ac. kr)  \nAbstract  \nI develop a Hamiltonian framework for Zk p-form gauge fields on arbitrary oriented cell complexes in arbitrary dimensions. Gauge qudits are defined by p-cells, charged boundary qudits by (p − 1)-cells, Gauss-law generators by boundary map ∂p, and magnetic checks by ∂p+1 . The same cellular structure produces local dressed Wilson operators, and at k = 2 a Calderbank–Shor–Steane check complex relevant to quantum error correction. I then specialize to p = 2, k = 2, where the magnetic 3-cell term is absent and the one-form Gauss-law can be solved exactly. The physical Hilbert space is parameterized by plaquette electric-flux variables, while the link configuration is reconstructed as the dynamical boundary of the evolving flux domains. The reduced Hamiltonian is an Ising-type plaquette model, where its local transverse-field term is the physical image of the boundary-dressed Wilson operator σzp Qℓ∈∂pτzℓ . A tube–cap quench compares two initial flux fillings with the same initial boundary loops. Exact diagonalization on 4 × 4 , 6× 4, and 5 × 5 tori finds that the cap loses 20–37% of its occupied-flux area, while the tube remains nearly pinned. A finite-size scaling locatesa dynamical crossover of tension-to-density ratio near (m/εE )c ≃ 1.89. The unreduced plaquette-plus-link encoding provides local Gauss-law checks and a direct digital implementation, while the reduced plaquette-only Hamiltonian supplies the exact benchmark. The result places the specific top-form discharge and the cosmological constant neutralization calculation inside a general higher-form Hamiltonian and coding framework.  \n1 Introduction  \n1.1 Exact dynamics of Gauss-law reduced two-form lattice model  \nIn this paper, built upon my previous series of works on Kalb-Ramond gauge theory [1–4], I develop two levels. Section 2.1 first formulates a compact p-form gauge Hamiltonian of gauge group G = Z k on an arbitrary oriented cell complex in arbitrary dimensions. The boundary maps define the Gauss-law generators, magnetic operators, and dressed Wilson operators. This formulation separates the general higher-form operator algebra from the particular top-form model (used below in the numerical calculation for flux discharge and cosmological constant neutralization) and exposes the sparse Gauss-law-check structure  \nused in gauge-symmetry-adapted quantum error detection (QEC) and gauge-covariant simulation [5 , 6] .  \nThe backbone of the present work remains the exact real-time evolution of the specialized Gauss-law-projected, G = Z2 Hamiltonian. Solving the one-form Gauss-law eliminates the link variables from the independent Hilbert space and leaves one qubit per plaquette. The eliminated links remain derived observables,  \nτxℓ = σxpL σxpR .  \nConsequently, the closed link loops are the time-dependent domain-wall boundaries of the evolving plaquette-flux configuration. They are dynamical in the same precise sense that a Gauss-law-reconstructed electric field is dynamical in reduced Schwinger-model Hamiltonian, although they are not independent matter coordinates.  \nThe quench begins from two distinct plaquette-flux product states having the same initial boundary loops and different fillings of the torus. The tube state occupies the strip between the loops; the cap state occupies the complementary strip. The reduced Hamiltonian then evolves the complete physical Hilbert space. No boundary geometry is held fixed after preparation. Local plaquette flips alter the adjacent derived boundary links automatically, so boundary loops appear, deform, merge, and disappear as consequences of the flux dynamics.  \nExact diagonalization on 4 × 4 , 6 × 4, and 5 × 5 tori provides the principal results. The continuum and unreduced l","cbCaillHRyqRvLNN","https://ap.wps.com/l/cbCaillHRyqRvLNN","pdf",824072,1,33,"English","en",105,"# Introduction\n## Exact dynamics of Gauss-law reduced two-form lattice model\n## Quantum simulation of lattice gauge theories: state of the art","[{\"question\":\"What Hamiltonian framework does the work develop for p-form gauge fields?\",\"answer\":\"It constructs a Hamiltonian formulation for Zk p-form gauge fields on arbitrary oriented cell complexes, with Gauss-law generators and magnetic checks defined through boundary maps ∂p and ∂p+1, and gauge qudits placed on p-cells and related charged boundary qudits on (p−1)-cells.\"},{\"question\":\"How is the one-form Gauss-law handled in the specialized case p=2 and k=2?\",\"answer\":\"For p=2,k=2 the magnetic 3-cell term is absent, and the one-form Gauss-law can be solved exactly, eliminating link variables from the independent Hilbert space and leaving one qubit per plaquette.\"},{\"question\":\"What do cap–tube quenches and exact diagonalization reveal about flux discharge?\",\"answer\":\"With the same initial boundary loops but different flux fillings, exact diagonalization on 4×4, 6×4, and 5×5 tori shows that the cap state loses about 20–37% of its occupied-flux area while the tube state remains nearly pinned, with finite-size scaling identifying a dynamical crossover in the tension-to-density ratio near (m/εE)c ≈ 1.89.\"}]",1784208432,83,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"p-form-gauge-dynamics-and-digital-quantum-simulation-flux-and-cosmological-constant-neutralization","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/p-form-gauge-dynamics-and-digital-quantum-simulation-flux-and-cosmological-constant-neutralization/86088/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What Hamiltonian framework does the work develop for p-form gauge fields?","Question",{"text":75,"@type":76},"It constructs a Hamiltonian formulation for Zk p-form gauge fields on arbitrary oriented cell complexes, with Gauss-law generators and magnetic checks defined through boundary maps ∂p and ∂p+1, and gauge qudits placed on p-cells and related charged boundary qudits on (p−1)-cells.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the one-form Gauss-law handled in the specialized case p=2 and k=2?",{"text":80,"@type":76},"For p=2,k=2 the magnetic 3-cell term is absent, and the one-form Gauss-law can be solved exactly, eliminating link variables from the independent Hilbert space and leaving one qubit per plaquette.",{"name":82,"@type":73,"acceptedAnswer":83},"What do cap–tube quenches and exact diagonalization reveal about flux discharge?",{"text":84,"@type":76},"With the same initial boundary loops but different flux fillings, exact diagonalization on 4×4, 6×4, and 5×5 tori shows that the cap state loses about 20–37% of its occupied-flux area while the tube state remains nearly pinned, with finite-size scaling identifying a dynamical crossover in the tension-to-density ratio near (m/εE)c ≈ 1.89.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & 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