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