B5: Modular Arithmetic I

Problem Statement

You are given integers $n$, $a$ and $L$.

Implement an oracle $O$ satisfying the following transition on a quantum circuit $\mathrm{qc}$ with $n+1$ qubits.

For arbitrary integer $k$ satisfying $0 \leq k < L$, the operation satisfies

Constraints

• $1 \leq n \leq 10$
• $0 \leq a < L \leq 2^n$
• Global phase is ignored in judge.
• Integers must be encoded by little-endian.
• The submitted code must follow the specified format:

from qiskit import QuantumCircuit
 
 
def solve(n: int, a: int, L: int) -> QuantumCircuit:
    qc = QuantumCircuit(n + 1)
    # Write your code here:
 
    return qc

Hints