A2. Generate equal superposition of four basis states
time limit per test
1 second
memory limit per test
256 megabytes
standard input
standard output

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