What is Quantum Computing and How Does it Work?


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What is Quantum Computing and How Does it Work?

  1. 1. What is quantum computing and how does it work? By Rachel McGreevy
  2. 2. What is Quantum Computing and why does it work? A traditional computer is based on the Turing machine, a theoretical computer originally designed by Alan Turing. This analogy of a computer uses an unlimited length of tape which is divided into small squares that can each hold the value of 0, 1 or be left blank. The device then reads the symbols from the tape which provides the machine with instructions of what to do1. During the years this model has helped to develop modern computers, which use microprocessors to provide instructions for the machine. These microprocessors consist of hundreds of transistors, which amplify an electric signal, and can therefore hold the values of 1 (on) and 0 (off). According to Moore’s law, the amount of transistors that can be used in a microprocessor in a traditional computer doubles every 18 months. This is expected to last until around 2020, but scientists suggest that a quantum computer is the next step in computer science. Instead of a processor, a quantum computer uses the quantum states of matter to process operations on data2. To understand how a quantum computer can work, understanding quantum physics is important. In 1927, a Belgian industrialist called Ernest Solvay sponsored a series of physics conferences which some of the greatest minds of the 20th century attended. Physicists including Albert Einstein, Max Planck, Niels Bohr, Louis De Broglie and Erwin Schrödinger came together to discuss certain topics of physics, and all would be associated with devising the fundamentals of quantum physics. Around this time, most other physicists were so sure of the nature of matter that any new ideas or theories formulated which opposed classical physics were not considered, as in classical physics there were several assumptions made about matter, causing new theories very hard to become accepted by others. However, there were several experiments whose results could not be explained by classical physics, so they looked to other theories to explain the results of the investigations. The combined theories to the results of these experiments formulated foundations of modern quantum physics3. Attendees of the Fifth Solvay Conference Standing; A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Deonder, E. Schrödinger, J.E Verschaffelt, W. Pauli, W. Heisenberg, R.H. Fowler, L. Brillouin Middle Row; P. Debyre, M Knudsen, W.L. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr Front Row; I. Langmuir, M. Planck, M. Curie, H.A. Lorentz, A. Einstein, P. Lanevin. Ch.E. Guye, C.T.R. Wilson, O.W. RichardsonP1
  3. 3. A problem was thought up by physicist Gustav Kirchhoff whereby a black-body – an object that absorbs any radiation that falls on it – emits a certain amount of radiation depending on the temperature of the body. It was observed that radiation was emitted at the greatest level around the middle of the electromagnetic spectrum in the visible light region. Classical physics theories suggested the result of the amount of energy emitted in the ultraviolet zone should reach infinity, which did not make sense. Max Planck hypothesised that energy is emitted in small amounts called quanta, and this theory accurately explained observations made from the black-body radiation experiment. Planck said that the amount of energy produced by the black-body is proportional to the frequency of the radiation so; E ∝f so E = hf (where h is equal to Planck’s constant – 6.63 x10-34) For this to be true, Planck had to assume that the matter the black-body consisted of did not absorb energy continuously, only in ‘packets’, which Planck called quanta. However, all scientists believed at this time that light travelled in waves, not quanta, so Planck’s theory was not accepted until years later when Einstein applied it to another experiment, where he explained the photoelectric effect.4 These experiments showed that light travels in photons – the smallest unit of light quanta - which have properties of both waves and particles. This concept is called wave-particle duality. One experiment that matches Planck’s theory was the double-slit experiment carried out by Thomas Young, which seemed to result in light acting like a wave at first. Young shined a light source on a partition with two thin slits in, and when he did so, thin bands of light would appear on the wall opposite. As the light from the original source passed through one of the slits, the slit would act like a new source and the light would spread out and eventually would interfere with the light spreading from the other slit. A diagram is shown below of the wave pattern of the light. As light spreads out from both of the slits, the light waves interfere with each other, causing constructive and destructive interference. Where waves meet in-phase, there would be constructive interference and the amplitude of the waves would be added – called superposition. Where waves meet in anti-phase – opposite points in the wave cycle – there would be destructive interference as the amplitudes of the waves would cancel each other outP2.
  4. 4. On the opposite wall, there would be a pattern of bands of light, and where the light shows there would be constructive interference. Although the results seem to show light travels in waves, when single photons were fired one at a time, after many photons had individually released, the results of the experiment are exactly the same as using a continuous light source emitting many photons at once. This experiment seemed to show that light quanta – or photons - displayed properties of both waves and particles.5 As shown by these experiments, it is pertinent to have a different set of rules for matter on a smaller scale, as particles tend to act differently than objects on a larger scale. Quantum physics is therefore the study of the behaviour of matter on atomic and subatomic levels. Particles do not tend to act the way they are expected to act and so we use the Copenhagen Interpretation to think about the state of matter at any given point. The Copenhagen Interpretation says that a quantum particle exists in all of its possible states at the same time, until it has been observed and is therefore in one of its possible states. The particle existing in all of the possible states at the same time is called coherent superposition. An example of this can be observed in Schrödinger’s theoretical cat experiment. In Schrödinger’s experiment, there would be a phial containing poison, some radioactive material, and a Geiger counter, along with a live cat placed and sealed in a box. The Geiger counter would detect any radioactive decay from the material, and was connected to a hammer. If the Geiger counter did detect radioactive decay, of which there is a completely random probability of happening, the hammer would be prompted to smash the phial containing the poison, and kill the cat. If there was no radioactive decay, the phial would not be smashed and the cat would live. In the hour that the experiment would happen, the cat’s definite state would be unknown as the cat could not be observed from inside the box, and therefore it exists in a superposition of both states - life and death6. A diagram of the theoretical experiment is show belowP3. We use this interpretation of particles to look at how a quantum computer could work.
  5. 5. Although previously theorised by Richard Feynman, in 1985, David Deutsch attended a lecture on the theory of computation, and realised that computers worked in accordance with the classical laws of physics, which had been improved with quantum theory, shown in the experiments mentioned above7. He proposed an extension of the original Turing Machine, renamed the Quantum Turing Machine, that worked by the laws of quantum physics, rather than classical physics. He suggested that a quantum computer that uses the quantum states of matter to calculate process would drastically increase computational power. A quantum computer uses spinning particles as processing power and due to the rules of quantum physics these particles exist in all states at once; so many processes can be calculated at the same time8. Instead of the traditional computers which use bits, or binary digits, to process instructions which can hold the value of 0 or 1, Deutsch suggested that a quantum computer would use a quibit, or a quantum binary digit, which represented quanta such as a particle, atom, electron or photon. The quibit would be able to hold the value of 0, 1 and a superposition of 0 and 1 - in other words, a quibit would hold the values of 0, 1 and any value in between all at the same time. This means that contrary to the classic Turing Machine, the Quantum Turing machine should be able to carry out many calculations at the same time, a concept is called parallelism9. We can represent a quibit using a Bloch sphere, pictured belowP4. The comparison between a quantum computer with a 3-bit register and a traditional computer with a 3-bit register can be used to show why a quantum computer can carry out many processes at once. In a traditional computer, a 3 bit register is able to represent any number from 0 up to 7 at once - as 23 = 8. A quantum computer with a 3 bit register is able to represent all numbers from 0-7 at the same time due to the state superposition in quibits10. A diagram of a 3 bit register in a quantum computer is shown belowP5. A Bloch sphere, used to physically represent a quibit.
  6. 6. When Deutsch created the concept of the quantum computer, scientists were not able to create a situation that would allow for superposition of particles to take place. Superposition of states can only happen when the particles are not being observed; this however means that other particles or atoms cannot interfere with the spinning particles. If the particles do interact with anything externally, the particle is forced into one of its possible states, and the particle is no longer in superposition7. A traditional computer uses a logic gate, which performs an operation that produces a single output, so represents a Boolean function – a yes or no output. Deutsch also realised that a quantum computer would have to use a quantum logic gate, which uses a number of quibits to perform its operations 11. One way scientists have tried to overcome the observation of particles in a quantum computer, and the particle falling into quantum decoherence, is using quantum entanglement. As established before, if a particle is observed, superposition collapses and they are forced into a definite state. If we apply an external force on two particles, they become entangled, and both particles will then possess the same qualities. When one of the particles is disturbed and begins to spin in one direction, the other particle will instantly take on similar properties to the first, but will spin in the opposite diresction12.This means that scientists will know the value of the quibits without looking at them, and therefore disturbing them, and the quibits will remain in their states13 Computer scientists were also unsure of how to program quantum computers to make calculations, as they weren’t sure what quantum computers were capable of. In 1994, even though no quantum computer existed at that time, Peter Shor created an algorithm that made use of its many possibilities. Shor’s algorithm will find the prime factors of any given number, however large the number may be. Although this may seem a small start, once implemented on a quantum computer, Shors algorithm can be used to break the infamous RSA cipher. The RSA cipher works using prime numbers, and is secure due to the fact that it would be impossible to computationally work out prime factors of a large amount many digit numbers. Shors algorithm could easily crack the cipher within minutes for a number with any number of digits, however could not be implemented without the invention of a working quantum computer14. In 1996, Lov Grover also created a quantum algorithm that will search an unsorted database at high speed. In 1996 there were still no quantum computers, but when it could be implemented on one, Grover’s algorithm could be used to crack a DES cipher, for which a list of all possible keys need to be searched and checked against the coded writing. A traditional computer can check around one million keys in 1 second, which means cracking the cipher would take more than one thousand years. A quantum computer implementing Grover’s algorithm would take around four minutes to complete exactly the same process7. In 2001, IBM created a quantum computer with a 7-bit register that used Shor’s algorithm to factor 15 into 3 x 5. A company called D-Wave created the first commercially available quantum computer with a 128-bit register in May 2011, costing around £10 million to buy15. Although the D-Wave One system only carries out one task, called discrete optimisation, it is a great step towards harnessing the power of quantum computing. Quantum computing has advanced tenfold in the past 20 years or so, and it will continue to do so. When quantum computers become common in every household, the things the human race will be able to do at the click of a mouse will be unthinkable. I think this is one of the most important fields, not only in computer science, but general science as well due to the possibilities it holds. One area in particular that will be aided by quantum computing is cryptography, to help crack the most difficult ciphers, and help encourage to make our information even more secure than it is today. I hope that one day in the not too distant future, a fully programmable quantum computer becomes available, as not only will it aid the developments of computer science, but help advance every aspect of our lives.
  7. 7. Ref. No. 1 Reference Title Reference Type Basic Information Date Published Evaluation http://computer.howstuffworks.com/ quantum-computer1.htm Website Explained the basics of how a traditional computer works No Publish Date Written by Kevin Bosnor & Jason Strickland The website is run by Discovery, so the information is likely to be correct. The website explained things basically so the source was useful to get basic information from. Reference Title Reference Type Basic Information Date Published Evaluation http://en.wikipedia.org/wiki/Quantu m_computer Website Explained the basics of how quantum computers work Last Modified on the 9th of October 2011, no original publish date. 3 Introducing Quantum Theory By J.P. McEvoy & Oscar Zarate Book 2007 Icon Books 4 http://isaacmmcphee.suite101.com/ max-planck-and-light-quantaa47790 Website Introduced how quantum physics was revealed with experiments and what quantum theory is Explained the blackbody radiation experiment and how Max Planck came to the conclusion that he did. 5 http://www.thekeyboard.org.uk/Qua ntum %20mechanics.htm Website Explained the double slit experiment Published 2004 Keith Mayes 6 http://science.howstuffworks.com/in novation /science-questions/quantumsuicide4.htm The Code Book By Simon Singh Website Explained Schrodinger’s cat experiment No Publish Date Josh Clark Wikipedia is an unreliable source as it is editable by other people. However, it was modified recently meaning it had up-to-date information, and I cross-referenced this with the first website I used. Wikipedia also uses complicated explanations so I had to use other websites to understand fully the explanation that was given. The book explained things well so it was easy to understand how quantum physics was discovered. The book went into detail in everything so it was simple for me to pick out the information I needed to write about. The website was written over 3 years ago so the information could have been out of date, and published by a member of the public who only writes with an interest on the topic, not a professional on the topic. To check the information was correct, I cross-referenced this with ‘introducing quantum theory’ (source 3) and a similar explanation was given in there. The article was written by a member of the public so information may be incorrect. It was also published 7 years ago so information could be out of date. The article however was very easy to understand and so was a fairly useful source. The website is run by Discovery, so the information is likely to be correct. The website explained things basically so the source was useful to get basic information from. Book Explained the introduction of quantum computers and how they can be programmed and used for cryptography 2000 Fourth Estate The book is written about the subject of cryptography, and not solely about quantum computers. This means the writing is aimed towards looking at the advancement in cryptography so may not have provided as much detail as it could have. The book is also 11 years old and quantum computers have advanced massively since then. 8 http://www.wisegeek.com/what-isquantum-computing.htm Website 11th July 2011 Ken Black 9 http://curiosity.discovery.com/quest ion/what-quantum-turing-machine Website Explained with more ease than other websites the basics of quantum computing Explains how quibits work compared to bits. 10 http://www.doc.ic.ac.uk/~nd/surpris e_97 Website Edited recently so information is likely to be up to date. However, wisegeek can also be edited by the public similarly to Wikipedia, so may not have been the most reliable source to use. Although there is no publish date, I used other websites to check that the information was valid before using it. The site is run by Discovery so the information is more than likely to be correct. This is an article posted by Imperial College London so is likely to be correct. There was more detail than needed so explanations were slightly Ref. No. 2 7 Explains how quibits work with superposition in a quantum computer March 15 2008 Published by Isaac McPhee No Publish Date How Stuff Works, by Discovery No Publish Date Simon Bone & Matias Castro