We give a quantum algorithm for computing an\u00a0\\(\\epsilon\\)-approximate Nash equilibrium of a zero-sum game in a\u00a0\\(m\\times n\\)\u00a0payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time\u00a0\\(O_\u02dc(\\sqrt{\u221a}\\sqrt{m+n}\\cdot {\\epsilon }_{-2.5}+{\\epsilon }_{-3})\\)\u00a0and outputs a classical representation of the\u00a0\\(\\epsilon\\)-approximate Nash equilibrium. This improves upon the best prior quantum runtime of \\(O_\u02dc(\\sqrt{\u221a}\\sqrt{m+n}\\cdot {\\epsilon }_{-3})\\)obtained by [vAG19] and the classic\u00a0\\(O_\u02dc((m+n)\\cdot {\\epsilon }_{-2})\\)\u00a0runtime due to [GK95] whenever\u00a0\\(\\epsilon =\\Omega ((m+n)_{-1})\\). We obtain this result by designing new quantum data structures for efficiently sampling from a slowly-changing Gibbs distribution.<\/p>\n","protected":false},"excerpt":{"rendered":"
We give a quantum algorithm for computing an\u00a0-approximate Nash equilibrium of a zero-sum game in a\u00a0\u00a0payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs in time\u00a0\u00a0and outputs a classical representation of the\u00a0-approximate Nash equilibrium. This improves upon the best prior quantum runtime of obtained by [vAG19] […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":[{"type":"text","value":"Adam Bouland","user_id":0},{"type":"text","value":"Yosheb Getachew","user_id":0},{"type":"text","value":"Yujia Jin","user_id":0},{"type":"user_nicename","value":"Aaron Sidford","user_id":"31120"},{"type":"text","value":"Kevin Tian","user_id":0}],"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"ICML 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