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Summary Quantum computing is contrasted with classical computing. The foundation of classical computing starts with a bit, a unit of information that can be in one of two states, 0 or 1. In quantum computing, the analogue of a bit is a qubit. For a qubit, 0 and 1 are just two possible states that a qubit could be in among others. The other possible physical states are motivated by possibilities of quantum systems such as superpositions. The idea behind a qubit as a means for computing has historically been speculative, but recent technological advances are bringing us closer to the realization of quantum computing. One of the main challenges in this area is to construct quantum systems that avoid decoherence as long as possible while manipulating the system. Another issue has to do with algorithms that serve as a foundation for security. If quantum computing systems are eventually constructed, they have the potential to undermine current encryption practices because many known intractable factoring problems would be turned into tractable ones.   Of more philosophical interest, the technological development of quantum computing has the potential to help us better understand the foundations of quantum physics.
Key works Much research was triggered by Shor 1994, who demonstrated how quantum algorithms could significantly speed up the factoring of large numbers into primes, and more generally exponentially speed up classical computation. Not everyone is so optimistic about the prospects of quantum speed ups, include Levin 2003
Introductions An introduction to the technical aspects of quantum computing and some of the philosophical issues can be found in Hagar 2008.
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  1. Guillaume Adenier, A. I͡U Khrennikov & Theo M. Nieuwenhuizen (eds.) (2006). Quantum Theory: Reconsideration of Foundations-3: Växjö, Sweden, 6-11 June 2005. American Institute of Physics.
    This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.
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  2. János A. Bergou (1999). Entangled Fields in Multiple Cavities as a Testing Ground for Quantum Mechanics. Foundations of Physics 29 (4):503-519.
    Entangled states provide the necessary tools for conceptual tests of quantum mechanics and other alternative theories. These tests include local hidden variables theories, pre- and postselective quantum mechanics, QND measurements, complementarity, and tests of quantum mechanics itself against, e.g., the so-called causal communication constraint. We show how to produce various nonlocal entangled states of multiple cavity fields that are useful for these tests, using cavity QED techniques. First, we discuss the generation of the Bell basis states in two entangled cavities, (...)
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  3. Robin Blume-Kohout & Wojciech H. Zurek (2005). A Simple Example of “Quantum Darwinism”: Redundant Information Storage in Many-Spin Environments. Foundations of Physics 35 (11):1857-1876.
  4. Todd A. Brun & Mark M. Wilde (2012). Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves. Foundations of Physics 42 (3):341-361.
    Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett (...)
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  5. Erwin Brüning, Thomas Konrad & F. Petruccione (eds.) (2012). Quantum Africa 2010: Theoretical and Experimental Foundations of Recent Quantum Technology, Umhlanga, South Africa, 20-23 September 2010. [REVIEW] American Institute of Physics.
    The conference Quantum Africa 2010 addressed recent advances, both theoretical and experimental, in the rapidly progressing field of quantum technologies. In particular progress in the foundations of quantum cryptography, quantum computing as well as quantum metrology was reported.
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  6. Jeffrey Bub (forthcoming). Quantum Computation From a Quantum Logical Perspective. .
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  7. Jeffrey Bub (2010). Quantum Computation: Where Does the Speed-Up Come From? In Alisa Bokulich & Gregg Jaeger (eds.), Philosophy of Quantum Information and Entanglement. Cambridge University Press. 231--246.
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  8. Jeffrey Bub (2008). Quantum Computation and Pseudotelepathic Games. Philosophy of Science 75 (4):458-472.
    A quantum algorithm succeeds not because the superposition principle allows ‘the computation of all values of a function at once’ via ‘quantum parallelism’, but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information‐processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I (...)
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  9. M. L. Dalla Chiara, A. Ledda, G. Sergioli & R. Giuntini (2013). The Toffoli-Hadamard Gate System: An Algebraic Approach. [REVIEW] Journal of Philosophical Logic 42 (3):467-481.
    Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of (...)
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  10. Maria Luisa Dalla Chiara, Roberto Giuntini, Hector Freytes, Antonio Ledda & Giuseppe Sergioli (2009). The Algebraic Structure of an Approximately Universal System of Quantum Computational Gates. Foundations of Physics 39 (6):559-572.
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  11. Ronald Chrisley (1995). Quantum Learning. In P. Pyllkkänen & P. Pyllkkö (eds.), New Directions in Cognitive Science. Finnish Society for Artificial Intelligence.
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  12. Ronald L. Chrisley, Learning in Non-Superpositional Quantum Neurocomputers.
    In both the search for ever smaller and faster computational devices, and the search for a computational understanding of biological systems such as the brain, one is naturally led to consider the possibility of computational devices the size of cells, molecules, atoms, or on even smaller scales. Indeed, it has been pointed out Braunstein, 1995] that if trends over the last forty years continue, we may reach atomic-scale computation by the year 2010 Keyes, 1988]. This move down in scale takes (...)
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  13. Tanner Crowder & Keye Martin (2012). Information Theoretic Representations of Qubit Channels. Foundations of Physics 42 (7):976-983.
    A set of qubit channels has a classical representation when it is isomorphic to the convex closure of a group of classical channels. From Crowder and Martin (Proceedings of Quantum Physics and Logic, Electronic Notes in Theoretical Computer Science, 2009), we know that up to isomorphism there are five such sets, each corresponding to either a subgroup of the alternating group on four letters, or a subgroup of the symmetric group on three letters. In this paper, we show that the (...)
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  14. Michael E. Cuffaro, On the Significance of the Gottesman-Knill Theorem.
    According to the Gottesman-Knill theorem, quantum algorithms utilising operations chosen from a particular restricted set are efficiently simulable classically. Since some of these algorithms involve entangled states, it is commonly concluded that entanglement is not sufficient to enable quantum computers to outperform classical computers. It is argued in this paper, however, that what the Gottesman-Knill theorem shows us is only that if we limit ourselves to the Gottesman-Knill operations, we will not have used the entanglement with which we have been (...)
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  15. Michael E. Cuffaro, On the Necessity of Entanglement for the Explanation of Quantum Speedup.
    Of the many and varied applications of quantum information theory, perhaps the most fascinating is the sub-field of quantum computation. In this sub-field, computational algorithms are designed which utilise the resources available in quantum systems in order to compute solutions to computational problems with, in some cases, exponentially fewer resources than any known classical algorithm. While the fact of quantum computational speedup is almost beyond doubt, the source of quantum speedup is still a matter of debate. In this paper I (...)
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  16. Michael E. Cuffaro (forthcoming). How-Possibly Explanations in Quantum Computer Science. Philosophy of Science.
    A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds, and in so doing to describe the possibility spaces associated with these processes. By doing this we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in (...)
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  17. Michael E. Cuffaro (2013). On the Physical Explanation for Quantum Computational Speedup. Dissertation, The University of Western Ontario
    The aim of this dissertation is to clarify the debate over the explanation of quantum speedup and to submit, for the reader's consideration, a tentative resolution to it. In particular, I argue, in this dissertation, that the physical explanation for quantum speedup is precisely the fact that the phenomenon of quantum entanglement enables a quantum computer to fully exploit the representational capacity of Hilbert space. This is impossible for classical systems, joint states of which must always be representable as product (...)
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  18. Michael E. Cuffaro (2012). Many Worlds, the Cluster-State Quantum Computer, and the Problem of the Preferred Basis. Studies in History and Philosophy of Science Part B 43 (1):35-42.
    I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds explanation of quantum computation is incompatible with the recently developed cluster state model of quantum computation. Based on these considerations I conclude that we should reject the many worlds explanation of quantum computation.
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  19. Jean-Michel Delhôtel (2001). On Bits and Quanta. Studies in History and Philosophy of Science Part B 32 (1):143-150.
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  20. David Deutsch, It From Qubit.
    Of John Wheeler’s ‘Really Big Questions’, the one on which the most progress has been made is It From Bit? – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other Questions, such as How Come Existence?, because it does not necessarily require a metaphysical answer. And unlike, say, Why The Quantum?, it does not require the discovery of new laws of nature: there was room for hope that it (...)
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  21. Michael Dickson (2007). Is Measurement a Black Box? On the Importance of Understanding Measurement Even in Quantum Information and Computation. Philosophy of Science 74 (5):1019–1032.
    It has been argued, partly from the lack of any widely accepted solution to the measurement problem, and partly from recent results from quantum information theory, that measurement in quantum theory is best treated as a black box. However, there is a crucial difference between ‘having no account of measurement' and ‘having no solution to the measurement problem'. We know a lot about measurements. Taking into account this knowledge sheds light on quantum theory as a theory of information and computation. (...)
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  22. J. Michael Dunn, Lawrence S. Moss & Zhenghan Wang (2013). Editors' Introduction: The Third Life of Quantum Logic: Quantum Logic Inspired by Quantum Computing. [REVIEW] Journal of Philosophical Logic 42 (3):443-459.
  23. A. Duwell (2003). The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation - D. Bouwmeester, A. Ekert and A. Zeilinger (Eds.); Germany, 2000, 314pp, US$ 54, ISBN 3-540-66778-. [REVIEW] Studies in History and Philosophy of Science Part B 34 (2):331-334.
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  24. Armond Duwell (2007). The Many-Worlds Interpretation and Quantum Computation. Philosophy of Science 74 (5):1007-1018.
    David Deutsch and others have suggested that the Many-Worlds Interpretation of quantum mechanics is the only interpretation capable of explaining the special efficiency quantum computers seem to enjoy over classical ones. I argue that this view is not tenable. Using a toy algorithm I show that the Many-Worlds Interpretation must crucially use the ontological status of the universal state vector to explain quantum computational efficiency, as opposed to the particular ontology of the MWI, that is, the computational histories of worlds. (...)
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  25. Bart D.’Hooghe & Jaroslaw Pykacz (2004). Quantum Mechanics and Computation. Foundations of Science 9 (4):387-404.
    In quantum computation non classical features such as superposition states and entanglement are used to solve problems in new ways, impossible on classical digital computers.We illustrate by Deutsch algorithm how a quantum computer can use superposition states to outperform any classical computer. We comment on the view of a quantum computer as a massive parallel computer and recall Amdahls law for a classical parallel computer. We argue that the view on quantum computation as a massive parallel computation disregards the presence (...)
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  26. Laura Felline (2010). Structural Explanation From Special Relativity to Quantum Information Theory. In M. D'Agostino, G. Giorello & F. Laudisa (eds.), SILFS New Essays in Logic and Philosophy of Science. College Pubblications.
  27. Eliseo Fernández (2008). A Triadic Theory of Elementary Particle Interactions and Quantum Computation (Review). Transactions of the Charles S. Peirce Society 44 (2):pp. 384-389.
  28. Hector Freytes (2010). Quantum Computational Structures: Categorical Equivalence for Square Root qMV -Algebras. Studia Logica 95 (1/2):63 - 80.
    In this paper we investigate a categorical equivalence between square root qMV-algehras (a variety of algebras arising from quantum computation) and a category of preordered semigroups.
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  29. Matjaz Gams (ed.) (1997). Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: IOS Press.
  30. Víctor Gómez Pin (1997). New Developments on Fundamental Problems in Quantum Physics, Oviedo, julio de 1996. Theoria 12 (1):203-204.
  31. Stanley P. Gudder (2001). Book Review: Quantum Computation and Quantum Information. By Michael A. Nielsen and Isaac L. Chuang. Cambridge University Press, Cambridge, United Kingdom, 2000, I–Xxv+676 Pp., $42.00 (Hardcover). [REVIEW] Foundations of Physics 31 (11):1665-1667.
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  32. Amit Hagar, To Balance a Pencil on its Tip: On the Passive Approach to Quantum Error Correction.
    Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists (...)
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  33. Amit Hagar (2011). The Complexity of Noise: A Philosophical Outlook on Quantum Error Correction. Morgan & Claypool Publishers.
    In quantum computing, where algorithms exist that can solve computational problems more efficiently than any known classical algorithms, the elimination of errors that result from external disturbances or from imperfect gates has become the ...
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  34. Amit Hagar, Quantum Computing. Stanford Encyclopedia of Philosophy.
    Combining physics, mathematics and computer science, quantum computing has developed in the past two decades from a visionary idea to one of the most fascinating areas of quantum mechanics. The recent excitement in this lively and speculative domain of research was triggered by Peter Shor (1994) who showed how a quantum algorithm could exponentially "speed up" classical computation and factor large numbers into primes much more rapidly (at least in terms of the number of computational steps involved) than any known (...)
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  35. Amit Hagar (2007). Quantum Algorithms: Philosophical Lessons. [REVIEW] Minds and Machines 17 (2):233-247.
  36. Amit Hagar & Alex Korolev (2007). Quantum Hypercomputation—Hype or Computation? Philosophy of Science 74 (3):347-363.
    A recent attempt to compute a (recursion‐theoretic) noncomputable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion‐theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.
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  37. Amit Hagar & Alexandre Korolev (2006). Quantum Hypercomputability? Minds and Machines 16 (1):87-93.
    A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.
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  38. Amit Hagar & Giuseppe Sergioli (forthcoming). Counting Steps: A Finitist Interpretation of Objective Probability in Physics. Epistemologia.
    We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical (...)
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  39. Stuart Hameroff, Search for Quantum and Classical Modes of Information Processing in Microtubules: Implications for “the Living State”.
    Dynamical activities within living eukaryotic cells are organized by microtubules, main structural components of the cytoskeleton and cylindrical polymers of the protein tubulin. Evidence and theoretical models suggest that states of tubulin may play the role of “bits” in classical microtubule computational automata. The advent of quantum information devices, key roles played by quantum processes in protein dynamics, and coherent ordering in the cell cytoplasm further suggest that microtubules may function as quantum computational devices, and that mesoscopic and macroscopic quantum (...)
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  40. Stuart Hameroff, Is DNA a Quantum Computer?
    A recent paper by Rieper, Anders and Vedral (arxiv.org/abs/1006.4053: The Relevance Of Continuous Variable Entanglement In DNA) suggests that quantum entanglement among base pairs in the DNA double helix stabilizes the molecule. A summary of their paper is reported in MIT Technology Review (http://www.technologyreview.com/blog/arxiv/25375/) is below..
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  41. Stuart R. Hameroff (2007). The Brain Is Both Neurocomputer and Quantum Computer. Cognitive Science 31 (6):1035-1045.
    _Figure 1. Dendrites and cell bodies of schematic neurons connected by dendritic-dendritic gap junctions form a laterally connected input_ _layer (“dendritic web”) within a neurocomputational architecture. Dendritic web dynamics are temporally coupled to gamma synchrony_ _EEG, and correspond with integration phases of “integrate and fire” cycles. Axonal firings provide input to, and output from, integration_ _phases (only one input, and three output axons are shown). Cell bodies/soma contain nuclei shown as black circles; microtubule networks_ _pervade the cytoplasm. According to the (...)
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  42. Stuart R. Hameroff, Consciousness, Whitehead and Quantum Computation in the Brain: Panprotopsychism Meets the Physics of Fundamental Spacetime Geometry.
    _dualism_ (consciousness lies outside knowable science), _emergence_ (consciousness arises as a novel property from complex computational dynamics in the brain), and some form of _panpsychism_, _pan-protopsychism, or pan-experientialism_ (essential features or precursors of consciousness are fundamental components of reality which are accessed by brain processes). In addition to 1) the problem of subjective experience, other related enigmatic features of consciousness persist, defying technological and philosophical inroads. These include 2) the “binding problem”—how disparate brain activities give rise to a unified sense (...)
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  43. Stuart R. Hameroff (2002). Quantum Computation in Brain Microtubules. Physical Review E 65 (6):1869--1896.
    Proposals for quantum computation rely on superposed states implementing multiple computations simultaneously, in parallel, according to quantum linear superposition (e.g., Benioff, 1982; Feynman, 1986; Deutsch, 1985, Deutsch and Josza, 1992). In principle, quantum computation is capable of specific applications beyond the reach of classical computing (e.g., Shor, 1994). A number of technological systems aimed at realizing these proposals have been suggested and are being evaluated as possible substrates for quantum computers (e.g. trapped ions, electron spins, quantum dots, nuclear spins, etc., (...)
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  44. Stuart R. Hameroff & Nancy J. Woolf (2003). Quantum Consciousness: A Cortical Neural Circuit. In Naoyuki Osaka (ed.), Neural Basis of Consciousness. John Benjamins.
  45. Clare Hewitt-Horsman (2009). An Introduction to Many Worlds in Quantum Computation. Foundations of Physics 39 (8):869-902.
    The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best (...)
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  46. M. J. (2001). On Bits and Quanta - Hoi-Kwong Lo, Sandu Popescu and Tim Spiller (Eds), Introduction to Quantum Computation and Information (Singapore: World Scientific, 1998), XI+348 Pp., ISBN 981-02-3399-X, £35, US$52. [REVIEW] Studies in History and Philosophy of Science Part B 32 (1):143-150.
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  47. Subhash Kak (1999). The Initialization Problem in Quantum Computing. Foundations of Physics 29 (2):267-279.
    The problem of initializing phase in a quantum computing system is considered. The initialization of phases is a problem when the system is initially present in a superposition state as well as in the application of the quantum gate transformations, since each gate will introduce phase uncertainty. The accumulation of these random phases will reduce the effectiveness of the recently proposed quantum computing schemes. The paper also presents general observations on the nonlocal nature of quantum errors and the expected performance (...)
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  48. Subhash C. Kak (1996). Information, Physics, and Computation. Foundations of Physics 26 (1):127-137.
    This paper presents several observations on the connections between information, physics, and computation. In particular, the computing power of quantum computers is examined. Quantum theory is characterized by superimposed states and nonlocal interactions. It is argued that recently studied quantum computers, which are based on local interactions, cannot simulate quantum physics.
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  49. Subhash C. Kak (1996). Speed of Computation and Simulation. Foundations of Physics 26 (10):1375-1386.
    This paper examines several issues related to information, speed of computation, and simulation of a physical process. It is argued that mental processes proceed at a rate close to the optimal based on thermodynamic considerations. Problems related to the simulation of a quantum mechanical system on a computer are reviewed. Parallels are drawn between biological and adaptive quantum systems.
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  50. Tien D. Kieu (2002). Quantum Hypercomputation. Minds and Machines 12 (4):541-561.
    We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.
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