Solution To Weekly Challenge: Problem 1

Ready to put your solutions to test?

Photo of a Linear particle accelerator taken at CERN (Geneva, Switzerland) by the author

In the last lesson, I challenged you to solve five problems to help you revisit the fundamental mathematics of quantum computing.

Weekly Challenge: 5 Exercises For The Quantum Mind

Here is the solution to the first problem.

---

Problem 1

The Pauli-X gate acts as a quantum NOT gate and functions to flip a qubit state.

The following matrix represents it:

Apply this gate to a qubit in state |0⟩ and a qubit in state |1⟩.

What will the resulting states be after the application?

---

Solution 1

Given the Pauli-X gate matrix:

We need to apply it to |0> and |1> which are represented by the following vectors:

Let’s first apply the Pauli-X gate to |0> :

The final result is:

Next, let’s apply the Pauli-X gate to |1> :

The final result is:

We confirm that applying the Pauli-X gate to |0> flips it to |1> and vice versa.

---

Message me or mention in the comments below if any of these steps are unclear. Check out the next post to find the solution to Problem 2!