Quantum Computer Science: A Very Short Introduction

Albert Einstein (1879 – 1955) 1921 Nobel Prize in Physics

Max Born (1882 – 1970) 1954 Nobel Prize in Physics

Niels Henrik David Bohr (1885 – 1962) 1922 Nobel Prize in Physics

Erwin Rudolf Josef Alexander Schrödinger (1887 – 1961) 1933 Nobel Prize in Physics

Werner Karl Heisenberg (1901 – 1976) 1932 Nobel Prize in Physics

Richard Phillips Feynman (1918 – 1988) 1965 Nobel Prize in Physics

John Stewart Bell (1928 – 1990)

Part A

Portmanteau(x) = linguistic blend(s) of words

An economist is an expert who will know tomorrow why the things he predicted yesterday didn’t happen today. Evan Esar, American humorist (1899 – 1995) Computers in the future may weigh no more than 1.5 tons. Popular Mechanics, 1949 I think there is a world market for maybe five computers. Thomas Watson, chairman of IBM, 1943

Paul Adrien Maurice Dirac (1902 – 1984) 1933 Nobel Prize in Physics

Alan Mathison Turing (1912 – 1954)

Claude Elwood Shannon (1916 – 2001)

Anton Zeilinger (1945)

Alain Aspect (1947)

David Elieser Deutsch (1953)

Life is complex – it has both real and imaginary parts. Anonymous

David Hilbert (1862 – 1943)

Charles Hermite (1822 – 1901)

Wolfgang Ernst Pauli (1900 – 1958)

Part B

Part C

Quantum Entanglement

Quantum Computer Science: A Very Short Introduction (3)

Nobel Prize in Physics (1979) Steven Weinberg (born: 1933) Nobel Prize in Physics (1979)

(The New York Review of Books, We naturally tend to think that reality can be described locally. I can say what is happening in my laboratory, and you can say what is happening in yours, but we don’t have to talk about both at the same time. But in quantum mechanics it is possible for a system to be in an entangled state that involves correlations between parts of the system that are arbitrarily far apart, like the two ends of a very long rigid stick. For instance, suppose we have a pair of electrons whose total spin in any direction is zero. In such a state, the wave function (ignoring everything but spin) is a sum of two terms: in one term, electron A has positive spin and electron B has negative spin in, say, the north direction, while in the other term in the wave function the positive and negative signs are reversed. The electron spins are said to be entangled. If nothing is done to interfere with these spins, this entangled state will persist even if the electrons fly apart to a great distance. However far apart they are, we can only talk about the wave function of the two electrons, not of each separately. Entanglement contributed to Einstein’s distrust of quantum mechanics as much or more than the appearance of probabilities. Strange as it is, the entanglement entailed by quantum mechanics is actually observed experimentally. But how can something so nonlocal represent reality? The Trouble with Quantum Mechanics by Steven Weinberg (The New York Review of Books, January 19, 2017) https://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/

Such an argument for elements of reality – predetermined values – was put forth in 1935 (in a different context) by Albert Einstein, Boris Podolski, and Nathan Rosen (EPR). The controversy and discussion it has given rise to has steadily increased over the past seven decades. The terms “incomplete” and “element of reality” originated with EPR. Today it is Einstein’s most cited paper. N. David Mermin, Quantum Computer Science – An Introduction (New York: Cambridge University Press, 2007, page 157)

EPR and the Bell inequality

Charlie Alice Bob

Spooky actions at a distance: Mermin’s mysterious device

Three unconnected parts The device: Three unconnected parts Detector A Source C Detector B

Detector A

Mermin’s device

Bell’s inequality tells us that regardless of how the instruction sets are distributed, in all runs of the experiment the same color must flash 55.5% of the time. But as the device actually operates, the same color flashes 50% of the time. The device violates Bell’s inequality. But Bell’s inequality is a consequence of the existence of instruction sets. Therefore instruction sets cannot exist. But instruction sets were the only explanation we were able to find for how lights can flash the same color when the switches had the same setting. So, how can they? Yet they do. That is the conundrum posed by the device – its sublime mystery. N. David Mermin, Boojums All The Way Through (pages 143 – 144). New York: Cambrige University Press, 1990.

The physics behind Mermin’s device – 1

The physics behind Mermin’s device – 2

The physics behind Mermin’s device – 3 The lights always flash the same color when the switches have the same setting because the detectors are then measuring the polarization of the two photons along the same direction. Postulate 1

The physics behind Mermin’s device – 4 The same color flashes as often as different ones. The switches have one of the settings: 12, 13, 21, 23, 31, or 32. Hence, the two disks will be at 60° to one another. So, the polarizations will be the same 25% of the time: cos(60°) = (1∕2) 2 = 1 4 . But then: 6 9 ×25%+ 3 9 ×100%= 1 6 + 1 3 = 1 2 =50% Postulate 2

Bibliography

Leonard Susskind and Art Friedman, Quantum Mechanics – The Theoretical Minimum. (London: Penguin Books, 2015) Eleanor Rieffel and Wolfgang Polak, Quantum Computing – A Gentle Introduction. (Cambridge, MA: The MIT Press, 2014)

Lecture Collection | The Theoretical Minimum: Quantum Mechanics https://www.youtube.com/watch?v=iJfw6lDlTuA&list=PL701CD168D02FF56F https://www.youtube.com/watch?v=a6ANMKRBjA8&list=PL701CD168D02FF56F&index=2 https://www.youtube.com/watch?v=-GO3SL5n30k&list=PL701CD168D02FF56F&index=3 https://www.youtube.com/watch?v=tRWBoossG0Y&list=PL701CD168D02FF56F&index=4 https://www.youtube.com/watch?v=sgQafF7tLSo&list=PL701CD168D02FF56F&index=5 https://www.youtube.com/watch?v=1cLZsUEzUDs&list=PL701CD168D02FF56F&index=6 https://www.youtube.com/watch?v=QuW24mTDB8s&list=PL701CD168D02FF56F&index=7 https://www.youtube.com/watch?v=x0m2sQuAr34&list=PL701CD168D02FF56F&index=8 https://www.youtube.com/watch?v=fTRKMAj5q_4&list=PL701CD168D02FF56F&index=9 https://www.youtube.com/watch?v=dYtyslPtK8Y&list=PL701CD168D02FF56F&index=10