Quantum Computing: Theoretical versus Practical Possibility
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An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is possible in principle—there are no known laws of Nature that prevent it—yet scaling up the few qubits demonstrated so far has proven to be exceedingly difficult. While this could be regarded merely as a technological or practical impediment, I argue that this difficulty might be a symptom of new laws of physics waiting to be discovered. I distinguish between “strong” and “weak” emergentist positions. The former assumes that a critical value of a parameter exists (one that is most likely related to the complexity of the states involved) at which the quantum-mechanical description breaks down, in other words, that quantum mechanics will turn out to be an incomplete description of reality. The latter assumes that quantum mechanics will remain as a universally valid theory, but that the classical resources required to build a real quantum computer scale up with the number of qubits, which hints that a limiting principle is at work.
KeywordsQuantum computing quantum information entanglement strong emergence weak emergence philosophy of physics history of physics
My research for this paper began under a John Templeton Fellowship, which allowed me to spend the summer of 2009 at the Institute of Quantum Optics and Quantum Information of the University of Vienna. I especially thank my hosts, Professor Anton Zeilinger and Professor Markus Aspelmeyer, who made this visit possible, and for many enlightening discussions with them and other scientists in the Institute. I am solely responsible, of course, for the (probably controversial) views I express. I also thank the Academy of Finland for financial support through Academy Research Fellowship 00857 and Projects 129896, 118122, 135135, and 141559. Finally, I thank an anonymous referee for helpful comments, and Roger H. Stuewer for his editorial work on my paper.
- 1.Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information (Cambridge: Cambridge University Press, 2000), pp. 87-90.Google Scholar
- 2.W.K. Wootters and W.H. Zurek, “A single quantum cannot be cloned,” Nature 299 (1982), 802–803.Google Scholar
- 3.Karthikeyan S. Kumar and G.S. Paraoanu, “A quantum no-reflection theorem and the speeding up of Grover’s search algorithm,” Europhysics Letters 93 (2011), 2005, p1-p4.Google Scholar
- 4.Arun Kumar Pati and Samuel L. Braunstein, “Impossibility of deleting an unknown quantum state,” Nature 404 (2000), 164-165.Google Scholar
- 5.A.M. Steane, “A quantum computer only needs one universe,” Studies in History and Philosophy of Modern Physics 34 (2003), 469-478.Google Scholar
- 6.Asher Peres, Quantum Theory: Concepts and Methods (Dordrecht, Boston, London: Kluwer Academic Publishers, 1995), p. 373ff.Google Scholar
- 7.W.G. Unruh, “Maintaining coherence in quantum computers,” Physical Review A 51 (1995), 992-997.Google Scholar
- 8.John Preskill, “Quantum computing: pro and con,” Proceedings of the Royal Society of London [A] 454 (1998), 469-486.Google Scholar
- 9.A number of high-profile scientists (Leonid Levin, Stephen Wolfram, Gerard ’t Hooft) have expressed doubts that quantum computing can be ever realized. For a review of some of these positions, see Scott Aaronson, STOC 04, Chicago, Illinois, June 13–15, 2004 or Scott Aaronson, website <http://arxiv.org/abs/quant-ph/0311039>. However, there is no decisive proof in either direction.
- 11.S. Wallentowitz, I.A. Walmsley, and J.H. Eberly, “How big is a quantum computer?” website <http://arxiv.org/abs/quant-ph/0009069>.
- 12.Paul Benioff, “Resource Limited Theories and their Extensions,” website <http://arxiv.org/abs/quant-ph/0303086>; P.C.W. Davies, “The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law,” in Cristian S. Calude, ed., Randomness and Complexity: From Leibniz to Chaitin (Singapore: World Scientific, 2007), pp. 68-87; see also website <http://arxiv.ort/abs/quant-ph/0703041>.
- 13.Johannes Kofler and Časlav Brukner, “Are there fundamental limits for observing quantum phenomena from within quantum theory?” website <http://arxiv.org/abs/1009.2654>.
- 14.Rolf Landauer, “The physical nature of information,” Physics Letters A 217 (1996), 188-193.Google Scholar
- 15.Eric W. Weisstein,”RSA-200 Factored,” MathWorld Headline News (May 10, 2005), website <http://mathworld.wolfram.com/news/2005-05-10/rsa-200/>.
- 17.G.S. Paraoanu, "Localization of the Relative Phase via Measurements," Journal of Low Temperature Physics 153 (2008), 285-293.Google Scholar
- 18.For a review, see A.J. Leggett, “Testing the limits of quantum mechanics: motivation, state of play, prospects,” Journal of Physics: Condensed Matter 14 (2002), R415-R451.Google Scholar
- 19.J.I. Korsbakken, F.K. Wilhelm and K.B. Whaley, “The size of macroscopic superposition states in flux qubits,” Europhys. Lett. 89 (2010), 30003, p1-p5.Google Scholar
- 20.Florian Marquardt, Benjamin Abel, and Jan von Delft, “Measuring the size of a quantum superposition of many-body states,” Phys. Rev. A 78 (2008), 012109, 1-5.Google Scholar
- 21.Erik Ramberg and George A. Snow, “Experimental Limit on a Small Violation of the Pauli Principle,” Phys. Lett. B 238 (1990), 438-441.Google Scholar
- 22.L. Diósi, “A Universal Master Equation for the Gravitational Violation of Quantum Mechanics,” Phys. Lett. A 120 (1987), 377-381; Roger Penrose, “On Gravity’s Role in Quantum State Reduction,” General Relativity and Gravitation 28 (1996), 581-600.Google Scholar
- 23.For a collection of such results, see, for example, website <http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/physics.htm>.
- 24.P.W. Anderson, “More is Different,” Science 177 (1972), 393-396.Google Scholar
- 25.Eugene P. Wigner, “Relativistic Invariance and Quantum Phenomena,” Reviews of Modern Physics 29 (1957), 255-268; reprinted in Symmetries and Reflections: Scientific Essays of Eugene P. Wigner (Bloomington and London: Indiana University Press, 1967), pp. 51-81, and in The Collected Works of Eugene Paul Wigner. Part B. Historical, Philosophical, and Socio-Political Papers. Vol. VI. Philosophical Reflections and Syntheses, ed. Jagdish Mehra (Berlin and Heidelberg: Springer-Verlag, 1995), pp. 415-445.Google Scholar