{"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":"43c060bd-17bc-5e82-9e7b-4dbf3b490954","task_key":"train--Challenge~5f61~5fmain","task_revision_id":"1","upstream_id":"Challenge_61_main","short_description":"We replace each of the $M/2+1$ vertices of an $M/2$-simplex with","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the values of T and P.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    T: int, evolution time T (rounded to the nearest integer)\\n    P: float, achievable probability P (with two decimal places) of getting basis $\\\\left|a\\\\right\\\\rangle$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    T = ...\\n    P = ...\\n    # ---------------------------------------------------------------\\n\\n    return T, P\",\"problem_description\":\"\\n# Problem setup:\\nWe replace each of the $M/2+1$ vertices of an $M/2$-simplex with\\na complete graph of $M/2$ vertices, resulting in a total of $M/2(M/2+1)$ vertices.\\n\\nThe Hamiltonian is given by\\n\\\\begin{equation}\\nH=-\\\\gamma A-|a\\\\rangle\\\\langle a|,\\n\\\\end{equation}\\nwhere $\\\\gamma$ is a tunable parameter, $A$ is the adjacency matrix of this graph, and each vertex of the graph corresponds to a basis for this Hamiltonian. The state $|a\\\\rangle$ is the marked vertex on this graph. We choose the initial state $|s\\\\rangle$ to be the equal superposition of all vertices. We want to choose the proper value of $\\\\gamma$, and let the system evolve for the appropriate duration of time such that, at the end of the process, the system is maximally concentrated at the state $\\\\left|a\\\\right\\\\rangle$.\\n\\n# Main problem:\\n\\nSuppose $M=200$. Find the evolution time $T$ (rounded to the nearest integer) and the achievable probability $P$ (to two decimal places) of getting basis $\\\\left|a\\\\right\\\\rangle$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}