Solve this RubiQ's Sphere

This is a basic problem to get accustomed to implementing one-qubit quantum circuit operations with QASM.

We spun a qubit in all directions.

To solve this RubiQ's Sphere problem, you need to rotate the state so it reads $|0\rangle$​ with probability 1 when ran regularly for more than 10 iterations.

To make it simpler, know that the solution will be just a  combination of the following gates.

z qubit[0];    // pi rotation about the Z-axis

x qubit[0];    // pi rotation about the X-axis

y qubit[0];    // pi rotation about the Y-axis

h qubit[0];    // The combination of two rotations, pi     about the Z-axis followed by pi/2 about the Y-axis

s qubit[0];    // S-gate, square root of Z gate

sdg qubit[0];  // conjugate of S-gate

t qubit[0];    // Phase-gate, conjugate of square root of S-gate

tdg qubit[0];  // conjugate of Phase-gate

Try some different gates until you get the solution!

Need some hints? Use at least ten samples (iterations). You only need a combination of X, Y, Z, and H gates. The order makes a difference. You only need two gates.

For more details on QASM, check out its here.