Implement a quantum oracle on N qubits which implements the following function: $$f(\vec{x}) = \vec{b} \cdot \vec{x} \mod 2 = \sum_{k=0}^{N-1} b_k x_k \mod 2$$, where $$\vec{b} \in \{0, 1\}^N$$ (a vector of N integers, each of which can be 0 or 1).

For an explanation on how this type of quantum oracles works, see Introduction to quantum oracles.

You have to implement an operation which takes the following inputs:

• an array of N qubits x in arbitrary state (input register), 1 ≤ N ≤ 8,
• a qubit y in arbitrary state (output qubit),
• an array of N integers b, representing the vector $$\overrightarrow{b}$$. Each element of b will be 0 or 1.

The operation doesn't have an output; its "output" is the state in which it leaves the qubits.

Your code should have the following signature:

见题面 Input 部分

见题面 Output 部分