G3. Palindrome checker oracle
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Implement a quantum oracle on $N$ qubits which checks whether the vector $\vec{x}$ is a palindrome (i.e., implements the function $f(\vec{x}) = 1$ if $\vec{x}$ is a palindrome, and 0 otherwise).

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

• an array of $N$ ($1 \le N \le 8$) 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.

Your code should have the following signature:

namespace Solution {    open Microsoft.Quantum.Primitive;    open Microsoft.Quantum.Canon;    operation Solve (x : Qubit[], y : Qubit) : Unit {        body (...) {            // your code here        }        adjoint auto;    }}