B3: Controlled Constant Addition

Problem Statement

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

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

For any pair of integers $(k, c)$ satisfying $0 \leq k < 2^n$ and $0 \leq c \leq 1$, the oracle satisfies

Constraints

• $1 \leq n \leq 10$
• $0 \leq a < 2^n$
• 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, QuantumRegister
 
 
def solve(n: int, a: int) -> QuantumCircuit:
    k, c = QuantumRegister(n), QuantumRegister(1)
    qc = QuantumCircuit(k, c)
    # Write your code here:
 
    return qc

Hints