Introducing quantum computing

Quantum computing isn't a subject that is as common as learning algebra or reading some of the literary classics. However, for most scientists and engineers or any other field that includes studying physics, quantum computing is part of the curriculum. For some of us who don't quite recall our studies in physics, or have never studied it, need not worry, as this section aims to provide you with information that will either refresh your recollection on the topic or at least perhaps help you understand what each of the principles used in quantum computing mean. Let's start with a general definition of quantum mechanics.

Quantum mechanics, as defined by most texts, is the study of nature at its smallest scale – in this case, the subatomic scale. The study of quantum mechanics is not new. Its growth began in the early 1900s by many physicists, whose names still chime in many of the current theories and experiments. The names of such physicists include Erwin Schrodinger, Max Plank, Werner Heisenberg, Max Born, Paul Dirac, and Albert Einstein, among others. As years passed, many other scientists expanded on the foundations of quantum mechanics and began performing experiments that would either prove, disprove, or oftentimes illustrate that there is no proof.

One of the more popular experiments is the double slit experiment. Although this is found in classical mechanics, it is referenced in quantum computing to describe the behavior of a quantum bit (qubit). It is in this experiment researchers were able to demonstrate that light (or photons) can be characterized as both waves and particles.

There were many distinct experiments that have been conducted over the years that illustrate this phenomenon, one of which was to fire particles through a double slit one at a time where at the other side of the double slit was a screen that captured, as a point, the location where each particle would hit. When only one slit was open, all the particles would appear as a stack of points directly in front of the slit, as shown in the following diagram:

Figure 4.1 - Single-slit experiment (image source: https://commons.wikimedia.org/wiki/File:SingleSlitDiffraction.GIF)

From the previous diagram, you can see that all the particles are captured in an area directly across the slit.

However, when the second slit was open, it was imagined that there would be an identical stack of points on the screen. But this was not the case, as what was captured appeared to be a formation altogether different than what would be expected from a particle. In fact, it had the characteristics of a wave in that the points on the screen seemed to display a diffraction pattern, as shown in the following diagram:

Figure 4.2 - Double-slit experiment (image source: https://commons.wikimedia.org/wiki/File:Double-slit.PNG)

From the previous diagram, you can see that all the particles are spread out from the center with interference gaps.

This diffraction pattern is caused by the interference of the light waves passing through the slits. Here, there are more points at the center of the screen than there are toward the outer ends of the observing screen. This wave particle phenomenon gave birth to lots of interesting research and development such as the Copenhagen interpretation, many-worlds interpretation, and the De Broglie-Bohm theory.

What this illustrated was that the light appeared as bands of light in certain areas of the board with some probability. By observing the preceding diagram, you can see that there is a higher probability that the electron fired from the gun will land in the center band of the screen as opposed to the outer bands. Also, note that due to interference, the spaces in between the bands that capture the electrons have less probability (blank areas between bands).

It is these effects of wave interference and probabilities that we will cover in this chapter, but first, we will start with the electron itself to understand superposition.