Abstract
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.
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Notes
I use the word “complexity” in a very general sense to cover, for example, high-complexity classes of problems (in the computational sense) and highly entangled many-particle states, including Schrödinger-cat states (superpositions of many-body states with distinct macroscopic properties). A mathematical formulation of quantum complexity would be valuable, but it is not clear what a generally useful one would be.
This is also true for versions of quantum computing that use measurement to produce the gates, such as the one-way quantum computer. Here some properties are actualized, but some must remain potential (that is, some quantum superpositions have to be preserved).
One can say that quantum tomography aims at extracting and mapping in a classical format all of the information contained in quantum states, while quantum computing attempts to extract only some information, namely, the solution to the problem. In this sense, quantum computing fares better. However, a quantum computer has to go through states that require a large amount of classical information to characterize. We do not have any warranty of how robust these states are and if they can be realized with reasonable resources.
RSA Laboratories, located in Bedford, Massachusetts, is the Security Division of EMC (Egan Marino Corporation).
This argument is weakened, of course, because to prepare a quantum state it is not really necessary, as I noted earlier, to have a one-to-one correspondence between quantum and classical states. Quantum states also can be prepared by having quantum systems interact with each other. However, to do this in a controllable way, precise classical-level manipulations of fields, potentials, and the like, are still required.
One can argue that states such as BCS (Bardeen-Cooper-Schrieffer) states look rather complex, yet there is no problem to obtain them because they are the ground states of simple Hamiltonians. But BCS states have a simple underlying symmetry: they are constructed from adding pairs of electrons with opposite momentum and spin to vacuum. Even so, BCS states actually are not so easily available: setting aside the low-temperature resources required, such states appear only in a few metals.
The record for the lowest temperature ever produced in a metal belongs to the Low Temperature Laboratory at Aalto University in Finland: 100 picokelvin (10−12 Kelvin). At the Massachusetts Institute of Technology, temperatures of the order of 500 picokelvin have been obtained recently in a different system, a Bose-Einstein condensate.
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Acknowledgments
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.
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G.S. Paraoanu received his Ph.D. degree in Physics at the University of Illinois at Urbana-Champaign in 2001 and a M.Sc. degree in Philosophy at the University of Bucharest in 1995. He currently is a senior scientist in the Low Temperature Laboratory at Aalto University, Finland, where his main scientific interests focus on degenerate quantum gases, mesoscopic superconducting devices, and the foundations of quantum mechanics.
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Paraoanu, G. Quantum Computing: Theoretical versus Practical Possibility. Phys. Perspect. 13, 359–372 (2011). https://doi.org/10.1007/s00016-011-0057-6
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DOI: https://doi.org/10.1007/s00016-011-0057-6