{"id":389,"date":"2026-06-04T04:00:00","date_gmt":"2026-06-04T04:00:00","guid":{"rendered":"https:\/\/futurenews24.com\/index.php\/2026\/06\/04\/2509-21570\/"},"modified":"2026-06-04T18:44:20","modified_gmt":"2026-06-04T18:44:20","slug":"2509-21570","status":"publish","type":"post","link":"https:\/\/futurenews24.com\/index.php\/2026\/06\/04\/2509-21570\/","title":{"rendered":"[2509.21570] Breaking $1\/\u03b5$ Barrier in Quantum Zero-Sum Video games: Generalizing Metric Subregularity for Spectraplexes"},"content":{"rendered":"<p><br \/>\n<\/p>\n<div id=\"content-inner\">\n<div id=\"abs\">\n<div class=\"dateline\">\n  [Submitted on 25 Sep 2025 (v1), last revised 2 Jun 2026 (this version, v2)]<\/div>\n<p>View a PDF of the paper titled Breaking $1\/epsilon$ Barrier in Quantum Zero-Sum Video games: Generalizing Metric Subregularity for Spectraplexes, by Yiheng Su and a couple of different authors<\/p>\n<p>    View PDF<br \/>\n    HTML (experimental)<\/p>\n<blockquote class=\"abstract mathjax\"><p>\n            <span class=\"descriptor\">Summary:<\/span>Quantum zero-sum video games present a framework for non-local video games, quantum interactive proofs, and quantum machine studying, the place gamers optimize a bilinear payoff over quantum states. In distinction to classical bilinear video games over polyhedral domains, for which gradient strategies obtain linear last-iterate convergence, comparable ensures over spectraplexes have remained open. Latest work achieved solely an $O(1\/varepsilon)$ average-iterate fee and steered that semidefinite geometry might preclude classical-style linear charges.<br \/>\nWe refute this obstruction. We show that quantum zero-sum video games admit algorithms with $O(log(1\/varepsilon))$ last-iterate convergence to Nash equilibrium. Particularly, matrix variants of Nesterov&#8217;s iterative smoothing and Optimistic Gradient Descent&#8211;Ascent match the asymptotic fee of the classical polyhedral case. The important thing technical ingredient is a brand new error-bound concept for semidefinite video games, establishing metric subregularity of the related monotone operator over spectrahedra regardless of the absence of polyhedral construction.<br \/>\nWe additionally give a geometrical characterization of Nash equilibria by way of slack operators, classifying strategic instructions as important, impartial, or non-essential. Underneath strict complementarity or nondegeneracy, this reduces to a pointy classical-style dichotomy. Lastly, we revisit Optimistic Matrix Multiplicative Weights Replace. By extending the Quantal Response Equilibrium framework to spectraplex video games, we show an $widetilde O(1\/varepsilon)$ last-iterate assure, whereas exhibiting that any $O(log(1\/varepsilon))$ speedup for this technique should rely upon a pure, dimension-dependent situation quantity. Experiments assist the theoretical image, with Optimistic Gradient Descent&#8211;Ascent outperforming Optimistic Matrix Multiplicative Weights Replace within the regimes studied.\n    <\/p><\/blockquote><\/div>\n<\/div>\n<div>\n<h2>Submission historical past<\/h2>\n<p> From: Pucheng Xiong [view email]                  [v1]<br \/>\n        Thu, 25 Sep 2025 20:51:13 UTC (106 KB)<br \/>\n    [v2]<br \/>\n        Tue, 2 Jun 2026 20:50:47 UTC (2,812 KB)\n<\/p><\/div>\n<p><br \/>\n<br \/><a href=\"https:\/\/arxiv.org\/abs\/2509.21570\">Source link <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>[Submitted on 25 Sep 2025 (v1), last revised 2 Jun 2026 (this version, v2)] View a PDF of the paper titled Breaking $1\/epsilon$ Barrier in Quantum Zero-Sum Video games: Generalizing Metric Subregularity for Spectraplexes, by Yiheng Su and a couple of different authors View PDF HTML (experimental) Summary:Quantum zero-sum video games present a framework for [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":392,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"http:\/\/arxiv.org\/static\/browse\/0.3.4\/images\/arxiv-logo-fb.png","fifu_image_alt":"","jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[],"jnews_override_bookmark_settings":[],"jnews_social_meta":[],"jnews_override_counter":[],"footnotes":""},"categories":[9],"tags":[619,620,618,622,623,624,431,626,625,621],"class_list":["post-389","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantum-computing","tag-619","tag-barrier","tag-breaking","tag-games","tag-generalizing","tag-metric","tag-quantum","tag-spectraplexes","tag-subregularity","tag-zerosum"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - 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