Quantum Computing Preliminaries

A (brief) history

Quantum theory is a science of the small: atoms, electrons, photons (light particles), and more. 

Some call it quantum theory, some call it quantum mechanics, some make a distinction between the two. We won't.

It is important to note that we will frequently refer to the non-quantum realm, i.e. the physical description of objects like baseballs, cars, lamps, etc. as classical physics. The classical world is the physical world we're used to in our everyday experience.

Quantum theory is one of humanity's crowning achievements, an extremely accurate and versatile theory.

It was developed near the beginning of the 20th century, coming roughly into its current form in the 1920s.

It is a beautiful and fascinating theory, that continues to bear sweet and delicious fruit for scientists, technologists, and engineers all around the world to this very day, and will likely continue to do so well into the future.

Quantum mechanics as an operating system

One can think of quantum theory like the operating system used on one's computer (Windows, macOS, etc).

That is, physical theories such as quantum electrodynamics, which model the interaction of atoms with light, and the standard model of particle physics, which describes and models the interactions between the most fundamental particles of nature, fit within the "operating system" that is quantum mechanics.

Computer programs, internet browsers, games, everything we use our computers for, all function within the bounds of a computer's operating system. That is, they obey the rules set out by the operating system.

Similarly, physical theories like quantum electrodynamics must obey the rules of quantum theory.

Some simple quantum mechanical systems 

It is worth keeping in mind a few simple physical systems as we proceed through the math of quantum theory. 

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