{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"critpt","formal_name":"CritPt","introduction":"研究水準の物理問題で、科学的理解と多段階の推論・計算を評価するベンチマークです。公開データには70の課題があり、問題文とコード雛形を組み合わせて解答を構成します。\n\nCritPt evaluates scientific understanding and multi-step reasoning and computation on research-level physics problems. Its public dataset contains 70 challenges with problem descriptions and code templates.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://critpt.com/","indexing_mode":"noindex"},"task_id":"1220bd73-c482-56b8-b22d-35ffda192359","task_key":"train--Challenge~5f68~5fmain","task_revision_id":"1","upstream_id":"Challenge_68_main","short_description":"The quantum $f$-divergence is defined by \\begin{align*}","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the value of $\\\\frac{d}{dt} D^{\\\\mathrm{std}}_f(\\\\rho_t \\\\|\\\\sigma)$ at $t = 0.5$.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    first_derivative: float, the first derivative $\\\\frac{d}{dt} D^{\\\\mathrm{std}}_f(\\\\rho_t \\\\|\\\\sigma)$ at $t = 0.5$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    first_derivative = ...\\n    # ---------------------------------------------------------------\\n\\n    return first_derivative\",\"problem_description\":\"# Problem setup:\\nThe quantum $f$-divergence is defined by \\\\begin{align*}\\n    D^{\\\\mathrm{std}}_f(\\\\rho \\\\|\\\\sigma) =  \\\\int_0^\\\\infty \\\\mathrm{tr}\\\\bigl[ (\\\\rho - \\\\sigma) \\\\frac{1}{L_\\\\rho + s R_\\\\sigma}(\\\\rho-\\\\sigma) \\\\bigr] d\\\\mu(s),\\n\\\\end{align*}\\nwhere $\\\\mu$ a positive measure on $(0,\\\\infty)$ such that $\\\\int_0^\\\\infty \\\\frac{1}{1+s} d\\\\mu(s) < \\\\infty$. We study the derivatives of the $f$-divergence. Let $\\\\rho_t = \\\\sigma + t(\\\\rho - \\\\sigma)$.\\n\\n# Main problem:\\n\\nCalculate $\\\\frac{d}{dt} D^{\\\\mathrm{std}}_f(\\\\rho_t \\\\|\\\\sigma)$ at $t = 0.5$. Please be as accurate as possible\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}