A2. Generate superposition of zero state and a basis state

Codeforces

IDCF1002A2

Time1000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Formal · Original

You are given _N_ qubits (1 ≤ _N_ ≤ 8) in zero state . You are also given a bitstring _bits_ which describes a non-zero basis state on _N_ qubits . Your task is to generate a state which is an equal superposition of and the given basis state: You have to implement an operation which takes the following inputs: * an array of qubits _qs_, * an arrays of boolean values _bits_ representing the basis state . This array will have the same length as the array of qubits. The first element of this array _bits_\[0\] will be _true_. The operation doesn't have an output; its "output" is the state in which it leaves the qubits. An array of boolean values represents a basis state as follows: the _i_\-th element of the array is true if the _i_\-th qubit is in state , and false if it is in state . For example, array _\[true; false\]_ describes 2-qubit state , and in this case the resulting state should be . Your code should have the following signature: namespace Solution { open Microsoft.Quantum.Primitive; open Microsoft.Quantum.Canon; operation Solve (qs : Qubit\[\], bits : Bool\[\]) : () { body { // your code here } } } [samples]

给定 #cf_span[N] 个量子比特（#cf_span[1 ≤ N ≤ 8]），初始处于零态。同时给定一个比特串 #cf_span[bits]，它描述了 #cf_span[N] 个量子比特上的一个非零基态。你的任务是生成一个状态，该状态是和给定基态的等权叠加：你需要实现一个操作，它接收以下输入：该操作没有输出；其“输出”是它作用后量子比特所处的状态。一个布尔值数组表示一个基态的方式如下：数组的第 #cf_span[i] 个元素为 true 表示第 #cf_span[i] 个量子比特处于状态，false 表示处于状态。例如，数组 _[true; false]_ 描述 2 量子比特态，此时最终状态应为。你的代码应具有以下签名： [samples]

**Definitions** Let $ N \in \mathbb{Z} $, $ 1 \leq N \leq 8 $, be the number of qubits. Let $ \mathbf{b} = (b_1, b_2, \dots, b_N) \in \{0,1\}^N $ be a non-zero bitstring representing a computational basis state $ |\mathbf{b}\rangle = |b_1 b_2 \dots b_N\rangle $. Let $ |0^N\rangle = |0\rangle^{\otimes N} $ denote the all-zero state. **Constraints** - $ \mathbf{b} \neq \mathbf{0} $ (i.e., at least one $ b_i = 1 $). **Objective** Implement a quantum operation that transforms the initial state $ |0^N\rangle $ into the normalized superposition: $$ |\psi\rangle = \frac{1}{\sqrt{2}} \left( |0^N\rangle + |\mathbf{b}\rangle \right) $$

API Response (JSON)

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      "content": "You are given _N_ qubits (1 ≤ _N_ ≤ 8) in zero state . You are also given a bitstring _bits_ which describes a non-zero basis state on _N_ qubits . Your task is to generate a state which is an equal ",
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    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
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