Задача . A2. Generate equal superposition of four basis states

You are given \(N\) qubits in the zero state \(|0...0 \rangle\). You are also given four distinct bit vectors which describe four different basis states on \(N\) qubits \(|\psi_i \rangle\).

Your task is to generate a state which is an equal superposition of the given basis states:

\(\)|S \rangle = \frac{1}{2} \big( |\psi_0 \rangle + |\psi_1 \rangle + |\psi_2 \rangle + |\psi_3 \rangle \big)\(\)

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

• an array of \(N\) (\(2 \le N \le 16\)) qubits,
• a two-dimensional array of Boolean values \(bits\) representing the basis states \(|\psi_i \rangle\). \(bits\) will have exactly 4 elements, each of \(bits[i]\) describing the basis state \(|\psi_i \rangle\). Each of \(bits[i]\) will have \(N\) elements, \(bits[i][j]\) giving the state of qubit \(j\) in the basis state \(|\psi_i \rangle\). Bit values true and false corresponding to \(|1 \rangle\) and \(|0 \rangle\) states, respectively; for example, for \(N = 2\) an array [false, true] will represent the basis state \(|01\rangle\). Each pair of \(bits[i]\) and \(bits[j]\) will differ in at least one position for \(i \neq j\).

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 (qs : Qubit[], bits : Bool[][]) : Unit {
        // your code here
    }
}