If there was one man who managed to excel at physics, to have incredible intuition along with great mathematical skill, and on top of all that be an excellent teacher and communicator, that was Richard P. Feynman [1]. His scientific legacy includes revolutionary contributions to quantum field theory and electrodynamics, inventing the widely used Feynman diagrams, or the theory of super-fluid Helium [2]. He even worked on the Manhattan project in his early career and like many greats, he took a stab at quantum gravity [3]. He was known as an excellent teacher, with great pedagogical skill, and his BBC show Fun to Imagine is still inspiring for anyone who watches its few episodes [4,5]. He was truly one of the the greatest physicists of the post-WW2 era.

One of his contributions, which often get overlooked, was to the first steps of quantum computing. In a lecture titled Simulating Physics with Computers, Professor Feynman talked about why physicists need computers, and what they require of these devices [6].

Physicists, and scientists in general, often used computers for simulations. Sometimes a given system is not accessible in the laboratory, or you are interested in understanding how it behaves by looking at its governing physical laws before your experiment. This implies a lot of mathematics. Computers are much better and faster than humans when it comes to the number of calculations needed. Feynman asked the following question: can a classical, universal computer simulate any physical system? And in particular, what about quantum systems?

As is usual in quantum mechanics, the problems here arise due to the superposition principle [7]. In a nutshell, quantum systems like electrons or photons can exist in a superposition of their possible observable states before a measurement. For example, imagine an electron for whatever reason is only allowed to be observed at two points A and B. Vaguely stated, the electron can be at A or B, or in a state which tells you that it can be at A or B with given probabilities. If you try to measure were the electron is, it turns up at one of the two points, even though it was at neither, or at both at the same time, before you performed the measurement [8].

What does this mean for computing though? Well, if you are to simulate the motion of our electron toy-model, you will always need to keep track of the two probabilities. That doesn’t seem too bad, but let’s consider multi-particle systems. For two electrons, you would need to keep track of the probability of having them both at A, both at B, one at A and one at B, or vice-versa (strictly speaking, things are more complicated than that, as embodied by the Pauli principle, but that is a story for another day). That makes up four probabilities to track. For three electrons, we would have to track eight. For four electrons, 16. For 10 electrons, we would need to track 1024 and for 20, a total of 1048576 probabilities. For realistic physical systems, made up of millions of electrons, this quickly gets out of hand.

For classical computers, the memory requirements for these calculations are too much. The true simulation of physical systems becomes intractable. This is where the interest in quantum computers started to grow [9]. Quantum systems, like qubits, can track these probabilities because it is in their very nature to do so! You could, in theory, simulate a many-particle quantum system with as many quantum particles, instead of the incredibly larger number of classical bits you would need to do the same on a normal computer. You could also encode the physics into operations on the qubits, like using logic gates circuits on bits [10]. Professor Feynman was definitely onto something!

The particle physicists at CERN had no intention of laying down the groundwork of the Internet or medical accelerators [11, 12]. All they wanted to do was smash particles into each other to see what they were made of. But as often happens, the needs of fundamental science end up spawning off new and interesting projects for humanity. Similarly, the interest today in quantum computers has grown far past the simulation needs of physicists. Nowadays we look at them for their potential to be much faster than classical computers, for the implementation of a new Internet and new security protocols [13]. As often happens though, this great idea was just a little something that appeared in the heads of one (or a few) of the great scientists of the past, only to grow without measure. For that I am sure we are all grateful.

[1] https://en.wikipedia.org/wiki/Richard_Feynman

[2] Richard Feynman, Ralph Leighton (contributor), Edward Hutchings (editor), Surely You’re Joking, Mr. Feynman!: Adventures of a Curious Character, 1985, W W Norton, ISBN 0–393–01921–7

[3] https://blogs.umass.edu/grqft/files/2014/11/Feynman-gravitation.pdf

[4] https://www.fractuslearning.com/2017/01/23/richard-feynman-education/

[5] http://www.bbc.co.uk/archive/feynman/

[6] https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf

[7] https://en.wikipedia.org/wiki/Quantum_superposition

[8] https://en.wikipedia.org/wiki/Wave_function_collapse

[9] https://web.archive.org/web/20150315071736/http://www.xootic.nl/magazine/jul-2003/west.pdf

[10] Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.)., 2011, Cambridge University Press, ISBN 13: 9781107002173.

[11] https://home.cern/about/updates/2013/03/ps1-million-engineering-prize-honours-web-pioneers

[12] https://home.cern/about/updates/2013/04/accelerators-medicine

[13] https://en.wikipedia.org/wiki/Quantum_computing#Potential

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