October 2016 – An Introduction to Quantum Computing and Music

Basic Concepts of Quantum Computing

Most phoenomenon we experience in our everyday lives, if not all, are governed by classical mechanics: from astronomical phonemonons, like sunsests or eclypses, to the mechanics of eletrical devices such as a television or a microwave oven. This is due to the fact that we live in a macro-world, and thus, are not aware of the laws that govern the dimensions of the atomic or even of the subatomic: the laws of the quantum world.

A classical computer (like the one you’re most likely reading this article with), works with basis on classical physics. This means that it generates an electrical current, whose voltage defines if that same current represents a 0 or a 1. That impulse is then conducted through a series of logic gates, and throught various combinations of countles impulses, the result is then shown on the display of the computer. We conclude, therefore, that at a physical level, the behaviour of the computer is well defined by electromagnetic phoenomenon, which are thoroughly explained by the Maxwell equations.

In the beginning of the 20th century, however, there was a revolution in physics: the quantum revolution. Through the efforts of people such as Max Planck, Erwin Schrödinger, Werner Heisenber, Niels Bohr, Louis de Broglie and Paul Dirac, we are now aware of some of the rules that govern the quantum world, such as non-localisation, superposition of quantum states, quantum entanglement and quantum fluctuations.

When these laws are applied to computation, we find that we obtain computational power that is exponentially greater than that which classical computing allows. It is how these phoenomenon work and how they can be applied to computation that we are going to explore in this page.

Introduction to this page

This webpage consists of two separate topics: Quantum computing and music (mostly classical). The reason why I chose two topics so far apart is because I am both an engineering student and a classically trained musician, and so I share a passion for both music and science. My posts will, therefore, be related to both topics: some of them regarding quantum computing, some of them regarding classical music.

My main goal with the music related part of my page is to present the “classical” world to the general public, free of any sort of bias there might be torwards classical music, and, if possible to bring people into the wonderful world that is classical music. I will also do brief and simple introductions to music theory so that all of you can capture some nuances and subtleties of some of the pieces I will share with you, otherwise undeteclable.

Overall, I hope you all become drawn into the world of classical music and that you free yourselves of some of the preconceived notions you might have about this genre. But above all, I hope you all have fun.

Regarding quantum computing, my main goal is to intruduce people to this concept, for the most part unknwon. However, I also intend to learn something myself, because, as I have said, I’m still a student and there’s a lot about this topic I’m still to discover.

I will introduce the basic concepts of quantum computing as simply as I can, an some of the concepts may be hard to grasp. I also intend to share some breakthroughs there might be in this area, as it’s still quite recent.

Perfect Harmony – Dmitri Shostakovich’s fugue in A major

In this post we’ll be discussing fugue by Shostakovich which consists of nothing but perfect harmony. First of all a fugue is a complicated musical form which we’ll not be talking about today. It may, however, appear in this web page when we discuss form.

First of all, what is harmony? Harmony is very simply the superposition of two or more notes together (for example, playing the notes C, E, and G (Do, Mi, Sol) at the same time). Now, in the study of harmony there are two groups: consonances and dissonances. Consonances are usually thought of as notes that sound good when they’re put together, and dissonances are usually thought of as notes that sound bad when put together.

The piece we’re going to be talking about relies only on perfectly consonant harmony, i.e. perfect major and perfect minor chords. Major and minor chords are groups of three notes put together, a third above each other. This means that if we take the diatonic scale: C, D, E, F, G, A, B (american notation) or Do, Re, Mi, Fa, Sol, La, Si (british notation), in order to obtain a perfect chord, we have to take every other note until we have three notes, and thus a perfect chord. e.g., in order to make a C (Do) major chord, we take Do (C), skip Re (D), Mi (E), skip Fa (F), Sol (G), thus making our perfect chord Do, Mi, Sol (C, E, G). For Mi (E) minor, we start with Mi (E), skip Fa (F), Sol (G), skip La (A), Si (B), thus making our perfect chord Mi, Sol, Si (E, G, B). We will not be discussing the difference between major and minor chords.

Dmitri Shostakovich (1906-1975) was one of the leading figures of 2oth century music worldwide. Living under the crushing dictatorial regime of Stalin, his music is notorious for its immense use of dissonance in order to represent the agony and oppression he felt on a daily basis (listen to his Symphonies nºs 5 and 10 and his string quartets nº8 and 15). In this piece, however, he makes use only of perfect consonance. The reason why is virtually unknown, although, in my opinion, it’s a symbol of hope, as if the consonance here represents a beacon of light in the middle of darkness.