Quantum Computing for Complete Beginners
Some have described the last several millennia of human dominion over the earth's resources as the anthropocene, deriving from the Greek "anthropo" meaning human, and "cene" meaning recent. The last century in particular has been dubbed the fourth industrial revolution, due to the pace of technological innovation ushered in by the advent of computers in the middle of the 20th century.
In the past seventy years, computation has transformed every aspect of society, enabling efficient production at an accelerated rate, displacing human labour from chiefly production to services, and exponentially augmenting information storage, generation, and transmission through telecommunications.
How did we get here? Fundamentally, technological advancement draws on existing science. Without an understanding of the nature of electromagnetism and the structure of atoms, we wouldn't have electricity and the integrated circuitry that power computers. It was only a matter of time, then, before we thought of exploiting the most accurate, fundamental description of physical reality provided by quantum mechanics for computation.
I became interested in quantum computation through both a strong interest in Physics and the nature of computation. If successful, quantum computation could usher in an unprecedented chapter in our information age by exponentially augmenting the efficiency of current computers. As someone interested in data, computation, and information science, understanding the rudiments of quantum information will not only equip you with a very basic understanding of quantum physics but also prepare you for the next major technological frontier of our information age.
Quantum Phenomena & Quantum Information
In order to understand the basics of computing, it is necessary to have a basic understanding of the physical phenomena that Quantum Computing exploits.
The phenomena in question are electron _spin and light polarization_, the latter being another term for photon spin. Recall that electrons are negatively charged subatomic particles that surround a positively charged nucleus, whereas photons are the particle equivalents of electromagnetism or light. Electron and photon spin are connected since they both refer to quantum properties that have no analogue in classical mechanics, which describes the scale of everyday objects.
Nonetheless, the easiest way to introduce spin is to draw a comparison to a classical property called angular momentum. Angular momentum refers to the rotational equivalent of linear momentum in a classical system, where momentum is calculated as the product of mass and velocity. As such, momentum is a vector quantity since it possesses both magnitude and direction. Angular momentum is represented as the cross product of the position and momentum vectors of a particle. Since angular momentum is a classical property, it admits of continuous values and can be expressed as a volume integral (generalized from the integral as the area under the curve in two dimensions).
Spin is often defined as intrinsic angular momentum. Recall that in classical mechanics force is defined as change in momentum. Furthermore the energy of the system is defined in terms of motion or the rate of change of motion, which presupposes mass. Unlike classical mechanics, Einstein's special theory of relativity ascribes intrinsic energy to rest mass through the equality E = mc². Similarly, intrinsic angular momentum is intimately bound up with the intrinsic energy state of a subatomic particle. In fact, it is a property that elementary particles possess whether or not they are actually rotating, that is, regardless of extrinsic factors like momentum and position, hence the qualifier intrinsic. Like classical angular momentum, quantum spin changes under rotations. However, unlike classical angular momentum, spin is quantized, which means that it only admits a discrete set of values.
The maximum spin of an elementary particle is given by the product of n (any integer of half integer n/2 values) and the reduced Planck's constant ℏ (h/2
