{"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":"aafd0ef3-cefb-527a-99d2-e82346e74ef8","task_key":"train--Challenge~5f70~5fmain","task_revision_id":"1","upstream_id":"Challenge_70_main","short_description":"Put $4n$ qubits on a lattice of $n$ rows and $4$ columns. Let…","config":"","split":"train","body":"{\"code_template\":\"def answer():\\n    r\\\"\\\"\\\"\\n    Return the value of $\\\\text{tr}(N^{\\\\otimes n}\\\\psi^{\\\\otimes 4})$.\\n\\n    Inputs\\n    ----------\\n    None\\n\\n    Outputs\\n    ----------\\n    trace: float, $\\\\text{tr}(N^{\\\\otimes n}\\\\psi^{\\\\otimes 4})$ when $|\\\\psi\\\\rangle$ is the $n$-qubit GHZ state for $n=3$\\n    \\\"\\\"\\\"\\n\\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\\n    trace = ...\\n    # ---------------------------------------------------------------\\n\\n    return trace\",\"problem_description\":\"# Problem setup:\\nPut $4n$ qubits on a lattice of $n$ rows and $4$ columns. Let $N:=\\\\int_{U(2)}U^{\\\\otimes 4}(S\\\\otimes S)(U^\\\\dagger)^{\\\\otimes 4}dU$ act on the $4$-qubit space of each row, where $S=|00\\\\rangle\\\\langle00|+|11\\\\rangle\\\\langle11|$, and $|\\\\psi\\\\rangle$ is a pure state on the $n$-qubit space of each column.\\n\\n# Main problem:\\nPlease compute $\\\\text{tr}(N^{\\\\otimes n}\\\\psi^{\\\\otimes 4})$ when $|\\\\psi\\\\rangle$ is the $n$-qubit GHZ state for $n=3$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://critpt.com/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}