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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 & Cuffaro 2015.
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  1. Scott Aaronson (2013). Quantum Computing Since Democritus. Cambridge University Press.
    Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.
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  2. D. Abrams & C. Williams (forthcoming). Quantum Algorithms. Complexity.
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  3. 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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  4. Patrick Allo (2003). Processen, veranderingen en interacties in computerwetenschappen en quantumfysica: Verslag van de SLI-2003 workshop, gehouden te Brussel, op 31 maart 2003. [REVIEW] Algemeen Nederlands Tijdschrift voor Wijsbegeerte 3.
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  5. Richard L. Amoroso (1997). The Theoretical Foundations for Engineering a Conscious Quantum Computer. In M. Gams, M. Paprzycki & X. Wu (eds.), Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: IOS Press
  6. Jürgen Audretsch (ed.) (2002). Verschränkte Welt. Faszination der Quanten. Wiley.
  7. 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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  8. 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.
  9. 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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  10. 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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  11. Jeffrey Bub (forthcoming). Quantum Computation From a Quantum Logical Perspective. Philosophical Explorations.
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  12. 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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  13. 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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  14. Jeffrey Bub, Quantum Entanglement and Information. Stanford Encyclopedia of Philosophy.
  15. Christian S. Calude, Michael J. Dinneen & Karl Svozil (2000). Reflections on Quantum Computing. Complexity 6 (1):35-37.
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  16. 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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  17. 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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  18. 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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  19. 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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  20. Richard Cleve, Artur Ekert, Leah Henderson, Chiara Macchiavello & Michele Mosca (1998). On Quantum Algorithms. Complexity 4 (1):33-42.
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  21. 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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  22. Michael 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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  23. 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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  24. Michael E. Cuffaro (forthcoming). On the Significance of the Gottesman-Knill Theorem. British Journal for the Philosophy of Science:axv016.
    According to the Gottesman-Knill theorem, quantum algorithms which utilise only the operations belonging to a certain restricted set are efficiently simulable classically. Since some of the operations in this set generate entangled states, it is commonly concluded that entanglement is insufficient to enable quantum computers to outperform classical computers. I argue in this paper that this conclusion is misleading. First, the statement of the theorem (that the particular set of quantum operations in question can be simulated using a classical computer) (...)
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  25. Michael E. Cuffaro (forthcoming). Reconsidering No-Go Theorems From a Practical Perspective. British Journal for the Philosophy of Science.
    I argue that our judgements regarding the locally causal models which are compatible with a given quantum no-go theorem implicitly depend, in part, on the context of inquiry. It follows from this that certain no-go theorems, which are particularly striking in the traditional foundational context, have no force when the context switches to a discussion of the physical systems we are capable of building with the aim of classically reproducing quantum statistics. I close with a general discussion of the possible (...)
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  26. Michael E. Cuffaro (2015). How-Possibly Explanations in Computer Science. Philosophy of Science 82 (5):737-748.
    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 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 subsequently asking a (...)
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  27. Michael E. Cuffaro (2014). Review Of: Christopher G. Timpson, Quantum Information Theory and the Foundations of Quantum Mechanics. [REVIEW] Philosophy of Science 81 (4):681-684,.
  28. 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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  29. 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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  30. 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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  31. 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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  32. 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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  33. Dennis Dieks, Décio Krause & Christian de Ronde (2014). Preface Special Issue Foundations of Physics. Foundations of Physics 44 (12):1245-1245.
    The foundations of quantum mechanics are attracting new and significant interest in the scientific community due to the recent striking experimental and technical progress in the fields of quantum computation, quantum teleportation and quantum information processing. However, at a more fundamental level the understanding and manipulation of these novel phenomena require not only new laboratory techniques but also new understanding, development and interpretation of the formalism of quantum mechanics itself, a mathematical structure whose connection to what happens in physical reality (...)
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  34. David P. DiVincenzo & Barbara M. Terhal (2005). Fermionic Linear Optics Revisited. Foundations of Physics 35 (12):1967-1984.
    We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible.
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  35. 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.
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  36. 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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  37. 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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  38. 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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  39. 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
  40. 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.
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  41. Richard P. Feynman (1986). Quantum Mechanical Computers. Foundations of Physics 16 (6):507-531.
    The physical limitations, due to quantum mechanics, on the functioning of computers are analyzed.
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  42. Donald R. Franceschetti & Elizabeth Gire (2013). Quantum Probability and Cognitive Modeling: Some Cautions and a Promising Direction in Modeling Physics Learning. Behavioral and Brain Sciences 36 (3):284-285.
    Quantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.
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  43. 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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  44. M. Gams (1997). The Theoretical Foundations for Engineering a Conscious Quantum Computer. In Matjaz Gams (ed.), Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: Ios Press 43--141.
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  45. Matjaz Gams (ed.) (1997). Mind Versus Computer: Were Dreyfus and Winograd Right? Amsterdam: IOS Press.
  46. Danko Georgiev (2007). Falsifications of Hameroff-Penrose Orch OR Model of Consciousness and Novel Avenues for Development of Quantum Mind Theory. Neuroquantology 5 (1):145-174.
    In this paper we try to make a clear distinction between quantum mysticism and quantum mind theory. Quackery always accompanies science especially in controversial and still under development areas and since the quantum mind theory is a science youngster it must clearly demarcate itself from the great stuff of pseudo-science currently patronized by the term "quantum mind". Quantum theory has attracted a big deal of attention and opened new avenues for building up a physical theory of mind because its principles (...)
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  47. Víctor Gómez Pin (1997). New Developments on Fundamental Problems in Quantum Physics, Oviedo, julio de 1996. Theoria 12 (1):203-204.
  48. Rowan Grigg, The Universal Lattice.
  49. 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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  50. 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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