B1: Polynomial Oracle

Problem Statement

For an integer $x \; (0 \leq x < 8)$, define $f(x) = x^2 + x + 1 \pmod{8}$.

Implement an $6$-qubit oracle $O$ on a quantum circuit $\mathrm{qc}$.

The oracle $O$ acts on basis states $\ket{x}\ket{y}$, where $0 \leq x < 8$ and $0 \leq y < 8$, as follows:

Here, $\oplus$ denotes the bitwise XOR operator.

Constraints

• 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() -> QuantumCircuit:
    x = QuantumRegister(3)
    y = QuantumRegister(3)
    qc = QuantumCircuit(x, y)
 
    # Write your code here:
 
    return qc

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