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A2: Generate Uniform Superposition State

Time Limit: 3 sec

Memory Limit: 512 MiB

Score: 200

Problem Statement

You are given an integer nn.
Implement the operation of preparing the uniform superposition state ∣A⟩\ket{A} from the zero state on a quantum circuit qc\mathrm{qc} with nn qubits.
The uniform superposition state ∣A⟩\ket{A} is defined as

∣A⟩=12n∑i=02n−1∣i⟩=12n(∣0...0⏟n⟩+...+∣1...1⏟n⟩).\begin{align} \ket{A} &= \frac{1}{\sqrt{2^n}} \sum_{i=0}^{2^n-1} \ket{i} \nonumber\\ & = \frac{1}{\sqrt{2^n}} (\ket{\underbrace{0...0}_n} + ... + \ket{\underbrace{1...1}_n}). \nonumber \end{align}

Constraints

  • 1≤n≤101 \leq n \leq 10
  • Changes in the global phase are ignored.
  • The submitted code must follow the specified format: ((format to be added during rendering))

Sample Input

  • n=2n = 2
    The implemented quantum circuit qc\mathrm{qc} should perform the following transformation.
∣00⟩→qc14(∣00⟩+∣10⟩+∣01⟩+∣11⟩)\ket{00} \xrightarrow{\mathrm{qc}} \frac{1}{\sqrt{4}} (\ket{00} + \ket{10} + \ket{01} + \ket{11})

Hints

Open
  • You can apply the quantum gate gg to all the qubits of the quantum circuit qc\mathrm{qc} as follows:
qc.g(range(n))

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