Quantum Computing

I hate the LinkedIn communication style, where even sending an email is considered a cornerstone achievement and a huge step forward for humanity. But I have to admit, seeing a real quantum computer in action is truly thrilling: doing the math to understand how and why it works is fascinating, but looking at the output of a real machine is pure satisfaction.

Read the instructions carefully prior to use

In the previous post, we saw how to rotate the density operator with respect to the x, y, and z axes, and we derived simple formulas using Pauli algebra. Building on those results, we can now derive an even more elegant and useful formula for performing rotations around an arbitrary axis. Let's see how!

In this post, we explore a topic already discussed in the previous post: the representation of the density operator on the Bloch sphere. We had observed how the Pauli matrices decompose the density operator; today, we look at something truly crucial in quantum computing: how the density operator evolves under a unitary operator and how this induces nothing but a pure rotation, thus representable on the Bloch sphere. Since the density operator represents the quantum state of t

You can’t approach quantum computing without becoming a black belt in rotations.

We have seen very little about a qubit, much more is to come, but for the time being let's see

Unlike spaces defined over a real field, in Hilbert spaces where quantum states are defined, the vector product (called the outer product) does not make much sense, because the concept of "creating" a vector perpendicular to the two input vectors of the operation is not defined. Still there is a room to define an outer product between vectors.

By the end of this post, you'll be able to visualise quantum states on a sphere. We'll write a very small script that will also allow you to initialise qubits on a real quantum machine!

I believe there is no topic more mistreated in mainstream tech communication than quantum computing.