D. Distinguish plus state and minus state

Codeforces

IDCF1001D

Time1000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Formal · Original

You are given a qubit which is guaranteed to be either in or in state. Your task is to perform necessary operations and measurements to figure out which state it was and to return 1 if it was a state or -1 if it was state. The state of the qubit after the operations does not matter. ## Input You have to implement an operation which takes a qubit 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 (q : Qubit) : Int { body { // your code here } } } [samples]

给定一个量子比特，其状态保证为 $\ket{0}$ 或 $\ket{1}$ 状态。你的任务是执行必要的操作和测量，以确定它原本处于哪种状态，并在它是 $\ket{1}$ 状态时返回 1，在它是 $\ket{0}$ 状态时返回 -1。操作后量子比特的状态无关紧要。你需要实现一个操作，该操作以量子比特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，该操作以量子比特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 (q : Qubit) : Int { body { // your code here } }} [samples]

**Definitions** Let $ \ket{\psi} \in \{ \ket{0}, \ket{1} \} $ be the unknown initial state of a qubit. **Objective** Design a quantum operation that, given $ \ket{\psi} $, returns: $$ \begin{cases} 1 & \text{if } \ket{\psi} = \ket{0} \\ -1 & \text{if } \ket{\psi} = \ket{1} \end{cases} $$ using quantum gates and a measurement in the computational basis. The final state of the qubit is irrelevant.

API Response (JSON)

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    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
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