D1. Oracle for f(x) = b * x mod 2

Codeforces

IDCF1002D1

Time1000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Formal · Original

Implement a quantum oracle on _N_ qubits which implements the following function: , where (a vector of _N_ integers, each of which can be 0 or 1). For an explanation on how this type of quantum oracles works, see [Introduction to quantum oracles](https://codeforces.com/blog/entry/60319). You have to implement an operation which takes the following inputs: * an array of _N_ qubits _x_ in arbitrary state (input register), 1 ≤ _N_ ≤ 8, * a qubit _y_ in arbitrary state (output qubit), * an array of _N_ integers _b_, representing the vector . Each element of _b_ will be 0 or 1. The operation doesn't have an output; its "output" is the state in which it leaves the qubits. Your code should have the following signature: namespace Solution { open Microsoft.Quantum.Primitive; open Microsoft.Quantum.Canon; operation Solve (x : Qubit\[\], y : Qubit, b : Int\[\]) : () { body { // your code here } } } [samples]

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：，其中（一个包含 #cf_span[N] 个整数的向量，每个整数为 0 或 1）。有关此类量子预言机的工作原理，请参阅量子预言机简介。你需要实现一个操作，它接受以下输入：该操作没有输出；其“输出”是它对量子比特所留下的状态。你的代码应具有以下签名： [samples]

**Definitions** Let $ N \in \mathbb{Z}^+ $ be the number of qubits. Let $ \mathcal{H} = (\mathbb{C}^2)^{\otimes N} $ be the Hilbert space of $ N $ qubits. Let $ \mathbf{x} = (x_1, x_2, \dots, x_N) \in \{0,1\}^N $ be a computational basis state. Let $ f: \{0,1\}^N \to \{0,1\} $ be a Boolean function defined by $ f(\mathbf{x}) = \bigoplus_{i=1}^N x_i $ (parity of $ \mathbf{x} $). **Constraints** The oracle operates on $ N $ qubits in the computational basis. The oracle must implement the unitary transformation: $$ U_f: |\mathbf{x}\rangle \mapsto (-1)^{f(\mathbf{x})} |\mathbf{x}\rangle $$ **Objective** Implement the unitary operator $ U_f $ such that for all $ \mathbf{x} \in \{0,1\}^N $: $$ U_f |\mathbf{x}\rangle = (-1)^{\bigoplus_{i=1}^N x_i} |\mathbf{x}\rangle $$

API Response (JSON)

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