C5: Modular Arithmetic IV

Problem Statement

You are given integers $n$ and $m$, and two positive integers $a$ and $L$ that are coprime.

Implement an operation that prepares a superposition state $\ket{A}$ from the zero state on a quantum circuit $\mathrm{qc}$ with $n + 2m + 1$ qubits.

The superposition state $\ket{A}$ is defined by

Constraints

• $1 \leq n \leq 5$
• $1 \leq m \leq 5$
• $1 \leq a < L \leq 2^m$
• 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, QuantumRegister
 
 
def solve(n: int, m: int, a: int, L: int) -> QuantumCircuit:
    x, y = QuantumRegister(n), QuantumRegister(2 * m + 1)
    qc = QuantumCircuit(x, y)
    # Write your code here:
 
    return qc