A3: Controlled Gate II

Problem Statement

Given an integer $n$, implement an $(n + 1)$-qubit oracle $O$ on a quantum circuit $\mathrm{qc}$.

The oracle $O$ acts on basis states $\ket{m}\ket{k}_n$, where $0 \leq m < 2$ and $0 \leq k < 2^n$, as follows:

• If $k = 0$,

• Otherwise,

Here, $\oplus$ denotes the XOR operator.

Constraints

• $1 \leq n \leq 10$
• The circuit depth must not exceed $4$.
• Integers must be encoded by little-endian.
• Global phase is ignored in judge.
• The submitted code must follow the specified format:

from qiskit import QuantumCircuit, QuantumRegister
 
 
def solve(n: int) -> QuantumCircuit:
    m, k = QuantumRegister(1), QuantumRegister(n)
    qc = QuantumCircuit(m, k)
    # Write your code here:
 
    return qc

Hints