{"raw_statement":[{"iden":"statement","content":"Implement a quantum oracle on _N_ qubits which implements the following function: , i.e., the value of the function is 1 if _x_ has odd number of 1s, and 0 otherwise."},{"iden":"input","content":"You have to implement an operation which takes the following inputs:\n\n*   an array of qubits _x_ (input register),\n*   a qubit _y_ (output qubit).\n\nThe operation doesn't have an output; the \"output\" of your solution is the state in which it left the qubits.\n\nYour code should have the following signature:\n\nnamespace Solution {\n    open Microsoft.Quantum.Primitive;\n    open Microsoft.Quantum.Canon;\n\n    operation Solve (x : Qubit\\[\\], y : Qubit) : ()\n    {\n        body\n        {\n            // your code here\n        }\n    }\n}"}],"translated_statement":[{"iden":"statement","content":"实现一个作用于 #cf_span[N] 个量子比特上的量子预言机，实现以下函数：即，当 #cf_span[x] 中包含奇数个 1 时，函数值为 1，否则为 0。\n\n你需要实现一个操作，该操作接收以下输入：\n\n该操作没有输出；你的解决方案的“输出”是其最终留下的量子比特状态。\n\n你的代码应具有以下签名：\n\n"},{"iden":"input","content":"你需要实现一个操作，该操作接收以下输入：一组量子比特 #cf_span[x]（输入寄存器），一个量子比特 #cf_span[y]（输出量子比特）。该操作没有输出；你的解决方案的“输出”是其最终留下的量子比特状态。你的代码应具有以下签名：namespace Solution {    open Microsoft.Quantum.Primitive;    open Microsoft.Quantum.Canon;    operation Solve (x : Qubit[], y : Qubit) : ()    {        body        {            // your code here        }    }}"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ N \\in \\mathbb{Z}^+ $ be the number of qubits.  \nLet $ \\mathcal{H} = (\\mathbb{C}^2)^{\\otimes N} $ be the Hilbert space of $ N $ qubits.  \nLet $ |x\\rangle \\in \\mathcal{H} $ denote a computational basis state corresponding to an $ N $-bit string $ x \\in \\{0,1\\}^N $.  \n\nLet $ f: \\{0,1\\}^N \\to \\{0,1\\} $ be the parity function:  \n$$\nf(x) = \\bigoplus_{i=1}^N x_i = \\text{parity}(x) = \n\\begin{cases}\n1 & \\text{if } |x|_1 \\text{ is odd} \\\\\n0 & \\text{otherwise}\n\\end{cases}\n$$\n\n**Objective**  \nImplement a unitary operator $ U_f: \\mathcal{H} \\to \\mathcal{H} $ such that for all $ |x\\rangle \\in \\{0,1\\}^N $:  \n$$\nU_f |x\\rangle = (-1)^{f(x)} |x\\rangle\n$$\n\n**Constraints**  \n- The operation acts only on the $ N $ input qubits.  \n- No ancilla qubits may be used unless explicitly permitted (assumed not allowed).  \n- The implementation must be exact and unitary.  \n- The \"output\" is the final state of the qubits; no measurement is performed.","simple_statement":null,"has_page_source":false}