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In this post we will look at three very important things: a theorem that represents a pillar of quantum computing — namely, the impossibility of cloning the states of a qubit; quantum tomography, which allows us to reconstruct the quantum state before the collapse of the wave function; and an application that uses a quantum circuit as a small neural network to approximate a qubit cloner.

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.

Concept Map

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.

This part might, at first glance, seem quite boring and involve a series of seemingly meaningless transformations of the problem and to don't get stuck we need to understand the rational behind it.

Warning: this post is only meant to give you a rough idea of Microsoft's claims about its so-called 'revolutionary' architecture. Keep in mind that simplification inevitably leads to mistakes.

In the previous post, we easily derived the solution for small angles of oscillation, but it is easy to observe that for angles greater than 4º, the solution is no longer suitable.

Last time we unveiled the true nature of the pendulum motion and we have seen its deep link with the elliptic integral.

This post might seem rather boring, as it is a topic covered in thousands of pages on the internet. What I have tried to do here is to approach the solution by providing all the steps, even the most trivial ones, in order to offer a self-contained mini-tutorial.

The pendulum is a beautiful example of how complexity can emerge from one of the simplest models. Its motion dynamics reveal fascinating aspects with close ties to the latest quantum computer architecture: the Majorana-1!