You are given two qubits which are guaranteed to be in one of the Bell states:
Your task is to perform necessary operations and measurements to figure out which state it was and to return the index of that state (0 for , 1 for etc.). The state of the qubits after the operations does not matter.
## Input
You have to implement an operation which takes an array of two qubits as an input and returns an integer.
Your code should have the following signature:
namespace Solution {
open Microsoft.Quantum.Primitive;
open Microsoft.Quantum.Canon;
operation Solve (qs : Qubit\[\]) : Int
{
body
{
// your code here
}
}
}
[samples]
你被给予两个量子比特，它们保证处于贝尔态之一：
你的任务是执行必要的操作和测量，以确定它是哪个态，并返回该态的索引（0 表示 ，1 表示 ，依此类推）。操作后量子比特的状态无关紧要。
你需要实现一个操作，该操作接受一个包含两个量子比特的数组作为输入，并返回一个整数。
你的代码应具有以下签名：
## Input
你需要实现一个操作，该操作接受一个包含两个量子比特的数组作为输入，并返回一个整数。你的代码应具有以下签名：namespace Solution { open Microsoft.Quantum.Primitive; open Microsoft.Quantum.Canon; operation Solve (qs : Qubit[]) : Int { body { // your code here } }}
[samples]
**Definitions**
Let $ \mathcal{H} = \mathbb{C}^2 \otimes \mathbb{C}^2 $ be the Hilbert space of two qubits.
Let $ \{ |\Phi^+\rangle, |\Phi^-\rangle, |\Psi^+\rangle, |\Psi^-\rangle \} $ be the Bell basis, defined as:
$$
\begin{aligned}
|\Phi^+\rangle &= \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle), \\
|\Phi^-\rangle &= \frac{1}{\sqrt{2}}(|00\rangle - |11\rangle), \\
|\Psi^+\rangle &= \frac{1}{\sqrt{2}}(|01\rangle + |10\rangle), \\
|\Psi^-\rangle &= \frac{1}{\sqrt{2}}(|01\rangle - |10\rangle).
\end{aligned}
$$
The input state $ |\psi\rangle \in \mathcal{H} $ is guaranteed to be one of these four Bell states.
**Objective**
Given $ |\psi\rangle \in \{ |\Phi^+\rangle, |\Phi^-\rangle, |\Psi^+\rangle, |\Psi^-\rangle \} $, determine $ i \in \{0,1,2,3\} $ such that:
$$
|\psi\rangle =
\begin{cases}
|\Phi^+\rangle & \text{if } i = 0, \\
|\Phi^-\rangle & \text{if } i = 1, \\
|\Psi^+\rangle & \text{if } i = 2, \\
|\Psi^-\rangle & \text{if } i = 3.
\end{cases}
$$
This is to be done via quantum operations and measurements, returning the index $ i $.
**Constraints**
- The operation must act on a two-qubit system in one of the four Bell states.
- Only unitary operations and projective measurements in the computational basis are permitted.
- The final state of the qubits after measurement is irrelevant.
- The output must be an integer $ i \in \{0,1,2,3\} $ corresponding to the identified Bell state.