Quantum mechanics enables us to build computers that are, in some ways, much more powerful than classical computers. Small, gated quantum computers and experimental quantum computers already exist, but the world might soon see the arrival of quantum computers capable of demonstrating quantum advantage over their classical counterparts. When that happens, it will leave little time for the lengthy process of migrating to new cryptographic algorithms, so it’s best to plan ahead and consider post-quantum cryptography now.
In this entry, the second on post-quantum cryptography, we delve into the history of quantum computing, its foundation in quantum mechanics, and the kind of complex problems quantum computers will be able to solve.
Brief history of computing
To better comprehend quantum mechanics, it helps to understand how mathematics evolved over time, and with it, our understanding of nature.
Early in history, people’s mathematical understanding of the world was simpler than now: at first, only natural numbers (1, 2, 3, 4, 5, etc.) were used to count. Later, negative numbers (…, -3, -2, -1, 0, 1, 2, 3, ….) were incorporated as well. Eventually, multiplication and division were needed, and these required the concept of fractions created from positive integers. These were classified as rational numbers.
Rational numbers serve well in many practical applications of physics or classical mechanics, where the goal is to measure or approximate something to a sufficient degree of accuracy. However, when the ancient Egyptians wanted to calculate the area of a circle, they tried using fractions in their formula, but the results were not quite accurate. Further examination revealed that a certain number, which will eventually be called pi (symbolized by π and has the value of 3.14159…), can instead be used for this operation. This sparked the idea that there are numbers that cannot be represented by fractions. We call such as real numbers because there’s a tacit assumption that they describe how nature works. So, for a long time, people believed that the world exists on a continuum of scales.
However, the advent of nuclear physics in the late 19th and early 20th centuries started to challenge this view. The smallest unit of matter was initially thought to be the atom, thus it was so named — the ancient Greek “atomos” translates to “indivisible,” or more literally “uncuttable.” In the late 19th century, however, Sir Joseph John Thompson discovered a sub-atomic particle, the electron, and proposed the ‘plum pudding’ model of an atom. In the early 20th century, Ernest Rutherford first theorized the existence of protons and neutrons in an atom’s nucleus, a fact then proven by James Chadwick. Rutherford proposed a model of the atom where the electrons orbited the nucleus like planets around the sun.
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