Category: Quantum computing

In quantum mechanics, the probabilistic replaces the deterministic. This means that, for instance, an electron can’t be in a well defined position. This is due to a small uncertainty regarding its speed and its position, which means that an electron can actually be in two places at once, pop in and out of existence, and teleport instantly from a place to another, amongst other strange phoenomena. We then stop talking about well defined states and enter the realm of probability, and about the superpositions of those same states, which are described in the Schrödinger equations.

In classical computing, an electrical impulse can either and exclusively represent a 0 or a 1, which are differentiated by their respective voltage (low voltage represents a 0, and a high voltage represents a 1). In quantum computing, however, since we can not know the state of a quantum object until we observe it, then what will happen is a superposition of all the possible states. If we attribute, for instance, the spin of an electron to a bit (spin up=1, spin down=0), we can not know its definite spin, and thus a superposition of all possible spins is created. The bit that is generated is called a quantum bit, or a “qubit”.

Let us now compare the computational power of classical computers and of quantum computers: If we take two bits, each one can only have the value of either 0 or 1. The possible combinations are, therefore, 00, 01, 10 and 11. If we take two electrons, since their spin can correspond to both 0 and 1 at the same time, the number of possible combinations is exponentially larger than the number of bits allowed by classical computing. This then implies a far greater computational power than even our best super computers are capable of.

There is, however, a problem with quantum computing: Even though multiple quantum states can coexist, when observed, only one of those states can be shown. What a quantum computer then does is choose the combination of qubits that best fits the goal of the user. For instance, when running a simulation, a quantum computer is capable of testing all the possible combinations at once, but only one of those combinations is showed. This shows us the immense power of quantum computers relative to classical computers which can only test one combination at a time.

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.