A1. Generate superposition of all basis states

Codeforces

IDCF1002A1

Time1000ms

Memory256MB

Difficulty—

English · Original

Chinese · Translation

Formal · Original

You are given _N_ qubits (1 ≤ _N_ ≤ 8) in zero state . Your task is to generate an equal superposition of all 2_N_ basis vectors on _N_ qubits: For example, * for _N_ = 1, the required state is simply , * for _N_ = 2, the required state is . You have to implement an operation which takes an array of _N_ qubits as an input and has no output. The "output" of the operation 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 (qs : Qubit\[\]) : () { 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。你的任务是生成在 #cf_span[N] 个量子比特上所有 #cf_span[2N] 个基矢的等权叠加态：例如，你需要实现一个操作，该操作以一个包含 #cf_span[N] 个量子比特的数组作为输入，且无输出。该操作的“输出”是其作用后量子比特所处的状态。你的代码应具有如下签名： [samples]

**Definitions** Let $ N \in \mathbb{Z} $ with $ 1 \leq N \leq 8 $. Let $ \mathcal{H} = (\mathbb{C}^2)^{\otimes N} $ be the Hilbert space of $ N $ qubits. Let $ \{|x\rangle \mid x \in \{0,1\}^N\} $ be the computational basis of $ \mathcal{H} $, with $ |x\rangle $ denoting the computational basis state corresponding to bitstring $ x $. **Constraints** The initial state of the system is $ |0\rangle^{\otimes N} $. **Objective** Implement a unitary operation $ U $ such that: $$ U |0\rangle^{\otimes N} = \frac{1}{\sqrt{2^N}} \sum_{x \in \{0,1\}^N} |x\rangle $$ The operation $ U $ acts on $ N $ qubits and has no classical output; the result is the final quantum state of the qubits.

API Response (JSON)

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      "content": "You are given _N_ qubits (1 ≤ _N_ ≤ 8) in zero state . Your task is to generate an equal superposition of all 2_N_ basis vectors on _N_ qubits: For example, *   for _N_ = 1, the required state is s",
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