Implement a quantum oracle on $N$ qubits which checks whether the number of bits equal to 1 in the input vector $\vec{x}$ is divisible by 3 (i.e., implements the function $f(\vec{x}) = 1$ if the number of $x_i = 1$ in $\vec{x}$ is divisible by 3, and 0 otherwise).

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

• an array of $N$ ($1 \le N \le 9$) qubits $x$ in an arbitrary state (input register),
• a qubit $y$ in an arbitrary state (output qubit),

and performs a transformation $|x\rangle|y\rangle \rightarrow |x\rangle|y \oplus f(x)\rangle$. The operation doesn't have an output; its "output" is the state in which it leaves the qubits. Note that the input register $x$ has to remain unchanged after applying the operation.

Your code should have the following signature:

Note: the operation has to have an adjoint specified for it; adjoint auto means that the adjoint will be generated automatically. For details on adjoint, see Operation Declarations.

You are not allowed to use measurements in your operation.

见题面 Input 部分

见题面 Output 部分