Element contents
Physics and Computation
Published online by Cambridge University Press: 20 August 2021
Summary
This Element has three main aims. First, it aims to help the reader understand the concept of computation that Turing developed, his corresponding results, and what those results indicate about the limits of computational possibility. Second, it aims to bring the reader up to speed on analyses of computation in physical systems which provide the most general characterizations of what it takes for a physical system to be a computational system. Third, it aims to introduce the reader to some different kinds of quantum computers, describe quantum speedup, and present some explanation sketches of quantum speedup. If successful, this Element will equip the reader with a basic knowledge necessary for pursuing these topics in more detail.
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- Online ISBN: 9781009104975Publisher: Cambridge University PressPrint publication: 23 September 2021
References
Aaronson, S. (2010). BQP and the polynomial hierarchy. In Proceedings of the Forty-Second ACM Symposium on Theory of Computing (pp. 141–150). New York: Association for Computing Machinery.Google Scholar
Aaronson, S. (2011). The equivalence of sampling and searching. In Kulikov, A. & Vershchagin, N. (eds.), Lecture notes in computer science (vol. 6651, pp. 1–14). Berlin, Heidelberg: Springer.Google Scholar
Aaronson, S. , & Ambainis, A. (2014). The need for structure in quantum speedups. Theory of Computing, 6, 133–166.Google Scholar
Aharonov, D., van Dam, W., Kempe, J. et al. (2007). Adiabatic quantum computation is equivalent to standard quantum computation. SIAM Journal on Computing, 37(1), 166–194.Google Scholar
Albash, T. , & Lidar, D. A. (2018, Jan). Adiabatic quantum computation. Rev. Mod. Phys., 90, 015002.Google Scholar
Ambainis, A. (2019). Understanding quantum algorithms via query complexity. In Sirakov, B., de Souza, P. N., & Viana, M. (eds.), Proceedings of the International Congress of Mathematicians (ICM2018) (pp. 3265–3285). World Scientific.Google Scholar
Anderson, N. G. (2019). Information processing artifacts. Minds and Machines, 29, 193–225.Google Scholar
Andréka, H., Madarász, J. X., Németi, I., Németi, P., & Székely, G. (2018). Relativistic computation. In Cuffaro, M. E. & Fletcher, S. C. (eds.), Physical perspectives on computation, computational perspectives on physics (pp. 195–216). Cambridge University Press.Google Scholar
Annovi, F. (2015). Exploring quantum speed-up through cluster-state computers (unpublished doctoral dissertation). University of Bologna.Google Scholar
Beals, R., Buhrman, H., Cleve, R., Mosca, M., & de Wolf, R. (2001, July). Quantum lower bounds by polynomials. Journal of the ACM, 48(4), 778–797.Google Scholar
Bennett, C. H., Bernstein, E., Brassard, G., & Vazirani, U. (1997). Strengths and weaknesses of quantum computing. SIAM Journal on Computing, 26(5), 1510–1523.Google Scholar
Bennett, C. H., & DiVincenzo, D. P. (2000). Quantum information and computation. Nature, 404(6775), 247–255.CrossRefGoogle ScholarPubMed
Bernstein, E. , & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on Computing, 26(5), 1411–1473.Google Scholar
Braun, D. , & Georgeot, B. (2006, Feb). Quantitative measure of interference. Physical Review A, 73, 022314.Google Scholar
Braun, D. , & Georgeot, B. (2008, Feb). Interference versus success probability in quantum algorithms with imperfections. Physical Review A, 77, 022318.CrossRefGoogle Scholar
Bub, J. (2010). Quantum computation: Where does the speed-up come from. In Bokulich, A. & Jaegger, G. (eds.), Philosophy of quantum information and entanglement (p. 231–246). Cambridge: Cambridge University Press.Google Scholar
Chalmers, D. J. (1996). Does a rock implement every finite-state automoton. Synthese, 108, 309–333.Google Scholar
Church, A. (1936). An unsolvable problem in elementary number theory. American Journal of Mathematics, 58(2), 345–363.Google Scholar
Church, A. (1937). Review of “A. M. Turing. On computable numbers, with an application to the Entscheidungsproblem.” Journal of Symbolic Logic, 2(1), 42–43.Google Scholar
Cleve, R., Ekert, A., Macchiavello, C., & Mosca, M. (1998). Quantum algorithms revisited. Proceedings of the Royal Society of London A, 454, 339–354.Google Scholar
Copeland, B. (2004). Computable numbers: A guide. In Copeland, B. (ed.), The essential Turing: Seminal writings in computing, logic, philosophy, artificial intelligence, and artificial life. Oxford: Oxford University Press.Google Scholar
Copeland, B. (2019). The Church-Turing thesis. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Spring 2019 ed.). Metaphysics Research Lab, Stanford University. http://https://plato.stanford.edu/archives/spr2019/entries/church-turing/.Google Scholar
Copeland, B., & Shagrir, O. (2007). Physical computation: How general are Gandy’s principles for mechanisms? Minds and Machines, 17, 217–231.Google Scholar
Copeland, B., Shagrir, O., & Sprevak, M. (2018). Zeus’s thesis, Gandy’s thesis, and Penrose’s thesis. In Cuffaro, M. E. & Fletcher, S. (eds.), Physical perspectives on computation, computational perspectives on physics. Cambridge: Cambridge University Press.Google Scholar
Cuffaro, M. E. (2012). Many worlds, the cluster-state quantum computer, and the problem of the preferred basis. Studies in History and Philosophy of Modern Physics, 43, 35–42.Google Scholar
Cuffaro, M. E. (2013). On the physical explanation for quantum speedup (unpublished doctoral dissertation). The University of Western Ontario, London, Ontario.Google Scholar
Cuffaro, M. E. (2015). How-possibly explanations in (quantum) computer science. Philosophy of Science, 82(5), 737–748.Google Scholar
Cuffaro, M. E. (2017). On the significance of the Gottesman–Knill theorem. The British Journal for the Philosophy of Science, 68(1), 91–121.CrossRefGoogle Scholar
Cuffaro, M. E. (2018). Universality, invariance, and the foundations of computational complexity in the light of the quantum computer. In Hansson, S. (ed.), Technology and mathematics: Philosophical and historical investigations (pp. 253–282). Springer.CrossRefGoogle Scholar
Cuffaro, M. E. (in press). The philosophy of quantum computing. In Miranda, E. R. (ed.), Quantum computing in the arts and humanities. Cham: Springer Nature.Google Scholar
Datta, A., Flammia, S. T., & Caves, C. M. (2005, Oct). Entanglement and the power of one qubit. Physical Review A, 72, 042316.Google Scholar
Davies, M. (2013). Three proofs of the undecidability of the Entscheidungsproblem. In Cooper, S. B. & Leeuwen, J. v. (eds.), Alan Turing: His work and impact (p. 49–52). San Diego: Elsevier Science.Google Scholar
Dean, W. (2016). Computational complexity theory. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Winter 2016 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2016/entries/computational-complexity/.Google Scholar
Del Mol, L. (2019). Turing machines. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Winter 2019 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2019/entries/turing-machine/Google Scholar
Deutsch, D. (1985). Quantum theory, the Church–Turing principle and the universal quantum computer. Proceedings of the Royal Society of London A, 400, 97–117.Google Scholar
Deutsch, D. , & Jozsa, R. (1992). Rapid solutions of problems by quantum computation. Proceedings of the Royal Society of London A, 439, 553–558.Google Scholar
Dewhurst, J. (2018). Computing mechanisms without proper functions. Minds and Machines, 28, 569–588.Google Scholar
Duwell, A. (2007). The many-worlds interpretation and quantum computation. Philosophy of Science, 74(5), 1007–1018.Google Scholar
Duwell, A. (2017). Exploring the frontiers of computation: Measurement based quantum computers and the mechanistic view of computation. In Bokulich, A. & Floyd, J. (eds.), Turing 100: Philosophical explorations of the legacy of Alan Turing (vol. 324, pp. 219–232). Cham: Springer.Google Scholar
Duwell, A. (2018). How to make orthogonal positions parallel: Revisiting the quantum parallelism thesis. In Cuffaro, M. E. & Fletcher, S. (eds.), Physical perspectives on computation, computational perspectives on physics. Cambridge: Cambridge University Press.Google Scholar
Earman, J., & Norton, J. (1993, March). Forever is a day – supertasks in Pitowski and Malament-Hogarth spacetimes. Philosophy of Science, 60(1), 22–42.Google Scholar
Ekert, A., & Jozsa, R. (1998). Quantum algorithms: entanglement-enhanced information processing. Philosophical Transactions of the Royal Society of London A, 356, 1769–1782.Google Scholar
Feynman, R. P. (1982). Simulating physics with computers. International Journal of Theoretical Physics, 21(6), 467–488.Google Scholar
Feynman, R. P. (1985, Feb). Quantum mechanical computers. Optics News, 11(2), 11–20.CrossRefGoogle Scholar
Fletcher, S. C. (2018). Computers in abstraction/representation theory. Minds and Machines, 28(3), 445–463.Google Scholar
Fortnow, L. (2003). One complexity theorist’s view of quantum computing. Theoretical Computer Science, 292, 597–610.Google Scholar
Freedman, M. H. , Kitaev, A. , & Larson, M. J. (2003). Topological quantum computation. Bulletin of the American Mathematical Society, 40, 31–38.Google Scholar
Frigg, R., & Nguyen, J. (2020). Scientific representation. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Spring 2020 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/spr2020/entries/scientific-representation/.Google Scholar
Gandy, R. (1980). Church’s thesis and principles for mechanisms. In Barwise, J., Keisler, H. J., & Kunen, K. (eds.), The Kleene symposium (vol. 101, pp. 123–148). Elsevier.Google Scholar
Godfrey-Smith, P. (2009, Aug 01). Triviality arguments against functionalism. Philosophical Studies, 145(2), 273–295.CrossRefGoogle Scholar
Gross, D., Flammia, S. T., & Eisert, J. (2009, May). Most quantum states are too entangled to be useful as computational resources. Physical Review Letters, 102, 190501.Google Scholar
Grzegorczyk, A. (1957). On the definitions of computable real continuous functions. Fundamenta Mathematicae, 44(1), 61–71.Google Scholar
Hagar, A., & Cuffaro, M. (2019). Quantum computing. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Winter 2019 ed. ). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/win2019/entries/qt-quantcomp/.Google Scholar
Harris, R. , Lanting, T. , Berkley, A. et al. (2009, Aug). Compound Josephson-junction coupler for flux qubits with minimal crosstalk. Physical Review B, 80, 052506.Google Scholar
Hewitt-Horsman, C. (2009). An introduction to many worlds in quantum computation. Foundations of Physics, 39(8), 869–902.Google Scholar
Hilbert, D., & Ackermann, W. (1928). Grundzüge der theoretischen Logik. Berlin: Springer.Google Scholar
Hillery, M. (2016, Jan). Coherence as a resource in decision problems: The Deutsch–Jozsa algorithm and a variation. Physical Review A, 93, 012111.CrossRefGoogle Scholar
Hogarth, M. L. (1992). Does general relativity allow an observer to view an eternity in a finite time? Foundations of Physics Letters, 5(2), 173–181. doi: https://doi.org/10.1007/BF00682813Google Scholar
Horsman, C. , Kendon, V. , & Stepney, S. (2017). The natural science of computing. Communications of the ACM, 60(8), 31–34.Google Scholar
Horsman, C. , Kendon, V. , Stepney, S. , & Young, J. P. W. (2017). Abstraction and representation in living organisms: When does a biological system compute? In Dodig-Crnkovic, G. & Giovangnoli, R. (eds.), Representation and reality in humans, other living organisms, and intelligent machines (pp. 91–116). Cham: Springer International Publishing.Google Scholar
Horsman, C. , Stepney, S., Wagner, R. C., & Kendon, V. (2014). When does a physical system compute? Proceedings of the Royal Society of London A, 470, 20140182.Google Scholar
Horsman, D. (2017). The representation of computation in physical systems. In Massimi, M., Romeijn, J. W., & Schurz, G. (eds.), EPSA15 selected papers (pp. 191–204). Chamml: Springer.Google Scholar
Horsman, D. , Kendon, B. , & Stepney, S. (2018). Abstraction/representation theory and the natural science of computation. In Cuffaro, M. E. & Fletcher, S. C. (eds.), Physical perspectives on computation (pp. 127–149). Cambridge: Cambridge University Press.Google Scholar
Horsman, D. C. (2015). Abstraction/representation theory for heterotic physical computing. Philosophical Transactions of the Royal Society of London A, 373, 20140224.Google Scholar
Johansson, N., & Larsson, J.. (2017). Efficient classical simulation of the Deutsch–Jozsa and Simon’s algorithms. Quantum Information Processing, 16(9), 233.Google Scholar
Johansson, N., & Larsson, J.. (2019). Quantum simulation logic, oracles, and the quantum advantage. Entropy, 21, 800.Google Scholar
Josza, R., & Linden, N. (2003). On the role of entanglement on quantum-computational speed-up. Proceedings of the Royal Society of London A, 459, 2011–2032.Google Scholar
Kalai, G. (2020). The argument against quantum computers. In Hemmo, M. & Shenker, O. (eds.), Quantum, probability, logic: The work and influence of Itamar Pitowsky (pp. 399–422). Chamml: Springer International Publishing.Google Scholar
Kato, T. (1950). On the adiabatic theorem of quantum mechanics. Journal of the Physical Society of Japan, 5(6), 435–439.Google Scholar
Kendon, V., Sebald, A., & Stepney, S. (2015). Heterotic computing: past, present, and future. Philosophical Transactions of the Royal Society of London A, 373, 20140225.Google Scholar
Kripke, S. A. (2013). The Church-Turing “thesis” as a special corollary of Gödel’s completeness theorem. In Copeland, B., Posy, C., & Shagrir, O. (eds.), Computability: Turing, Gödel, Church, and beyond (p. 77–104). Cambridge, MA: Massachusetts Institute of Technology Press.Google Scholar
Ladyman, J. (2009). What does it mean to say that a physical system implements a computation? Theoretical Computer Science, 410, 376–383.Google Scholar
Lahtinen, V., & Pachos, J. K. (2017). A short introduction to topological quantum computation. SciPost Phys., 3, 021.Google Scholar
Lloyd, S. (1999, Dec). Quantum search without entanglement. Physical Review B, 61, 010301.Google Scholar
Longino, H. E. (1990). Science as social knowledge: Values and objectivity in scientific inquiry. Princeton: Princeton University Press.Google Scholar
Machamer, P., Darden, L., & Craver, C. F. (2000). Thinking about mechanisms. Philosophy of Science, 67(1), 1–25.Google Scholar
Maroney, O. (2009). Information processing and thermodynamic entropy. In Zalta, E. N. (ed.), The Stanford encyclopedia of philosophy (Fall 2009 ed.). Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/archives/fall2009/entries/information-entropy/.Google Scholar
Maroney, O. J. E., & Timpson, C. G. (2018). How is there a physics of information? On characterizing physical evolution as information processing. In Cuffaro, M. E. & Fletcher, S. C. (eds.), Physical perspectives on computation, computational perspectives on physics (pp. 103–126). Cambridge University Press.Google Scholar
Meyer, D. A. (2000, Aug). Sophisticated quantum search without entanglement. Physical Review Letters, 85, 2014–2017.Google Scholar
Milkowski, M. (2013). Explaining the computational mind. Cambridge, MA: Massachusetts Institute of Technology Press.Google Scholar
Neilsen, M., & Chuang, I. (2000). Quantum computation and quantum infomation. Cambridge: Cambridge University Press.Google Scholar
Piccinini, G. (2008). Computation without representation. Philosophical Studies, 137(2), 205–241.Google Scholar
Piccinini, G. (2015). Physical computation: A mechanistic account. Oxford: Oxford University Press.Google Scholar
Piccinini, G., & Bahar, S. (2013). Neural computation and the computational theory of cognition. Cognitive Science, 34, 453–488.Google Scholar
Pitowsky, I. (1990). The physical Church thesis and physical computational complexity. Iyyun, 39, 81–99.Google Scholar
Pitowsky, I. (2002). Quantum speed-up of computations. Philosophy of Science, 69(3), S168–S177.Google Scholar
Pitowsky, I. (2007). From logic to physics: How the meaning of computation changed over time. In Cooper, S. B., Löwe, B., & Sorbi, A. (eds.), Computation and logic in the real world (pp. 621–631). Berlin, Heidelberg: Springer Berlin Heidelberg.Google Scholar
Pour-El, M. B., & Richards, I. (1981). The wave equation with computable initial data such that its unique solution is not computable. Advances in Mathematics, 39(3), 215–239.Google Scholar
Putnam, H. (1988). Representation and reality. Cambridge, MA: Massachusetts Institute of Technology Press.Google Scholar
Raussendorf, R., & Briegel, H. (2001). A one-way quantum computer. Physical Review Letters, 86(5188).Google Scholar
Raz, R., & Tal, A. (2019). Oracle separation of BQP and PH. In Proceedings of the 51st annual ACM SIGACT symposium on theory of computing (pp. 13–23). New York: Association for Computing Machinery.Google Scholar
Rescorla, M. (2014). A theory of computational implementation. Synthese, 191, 1277–1307.Google Scholar
Roland, J., & Cerf, N. J. (2002, Mar). Quantum search by local adiabatic evolution. Physical Review A, 65, 042308.Google Scholar
Scheutz, M. (1999). When physical systems realize functions Mind and Machines, 9, 161–196.Google Scholar
Schweizer, P. (2019). Computation in physical systems: A normative mapping account. In Berkich, D. & d’Alfonso, M. (eds.), On the cognitive, ethical, and scientific dimensions of artificial intelligence (vol. 134, pp. 27–47). Chamml: Springer.Google Scholar
Searle, J. R. (1992). The rediscovery of the mind. Cambridge, MA: Massachusetts Institute of Technology Press.Google Scholar
Shinbrot, T., Grebogi, C., Wisdom, J., & Yorke, J. A. (1992). Chaos in a double pendulum. American Journal of Physics, 60(6), 491–499.CrossRefGoogle Scholar
Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th Annual Symposium on Foundations of Computer Science (pp. 124–134).Google Scholar
Sieg, W. (1994). Mechanical procedures and mathematical experience. In George, A. (ed.), Mathematics and mind (pp. 71–117). Oxford University Press.Google Scholar
Sieg, W. (2002a). Calculations by man and machine: conceptual analysis. In Sieg, W., Sommer, R., & Tallcot, C. (eds.), Reflections on the foundations of mathematics: Essays in honor of Solomon Feferman (pp. 390–409). CRC Press.Google Scholar
Sieg, W. (2002b). Calculations by man and machine: mathematical presentation. In Gärdenfors, P., Woleñski, J., & Kajania-Placek, K. (eds.), In the scope of logic, methodology, and philosophy of science (vol. 1, pp. 247–262). Netherlands: Kluwer Academic Publishers.Google Scholar
Spekkens, R. W. (2007). Evidence for the epistemic view of states. Physical Review A, 75, 032110.Google Scholar
Sprevak, M. (2018). Triviality arguments about computational implementation. In Sprevak, M. & Colombo, M. (eds.), Routledge handbook of the computational mind (pp. 175–191). London: Routledge.Google Scholar
Stahlke, D. (2014, Aug). Quantum interference as a resource for quantum speedup. Physical Review A, 90, 022302.Google Scholar
Steane, A. (2003). A quantum computer needs only one universe. Studies in History and Philosophy of Modern Physics, 34, 469–478.Google Scholar
Timpson, C. G. (2013). Quantum information theory and the foundations of quantum mechanics. Oxford: Oxford University Press.Google Scholar
Timpson, C. G., & Brown, H. R. (2005). Proper and improper separability. International Journal of Quantum Information, 3(4), 679–690.Google Scholar
Turing, A. (1936). On computable numbers, with an application to the Entscheidungsproblem. Proceedings of the London Mathematical Society, 42(1), 230–265.Google Scholar
Turing, A. (1937). Computability and λ-definability. The Journal of Symbolic Logic, 2(4), 153–163.Google Scholar
van Fraassen, B. C. (2006). Representation: The problem for structuralism. Philosophy of Science, 73(5), 536–547.Google Scholar
Vollmer, H. (1999). Introduction to Circuit Complexity: A Uniform Approach. Italy: Springer-Verlag.Google Scholar
Wallace, D. (2012). The emergent multiverse: Quantum theory according to the Everett interpretation. Oxford: Oxford University Press.Google Scholar
Yoran, N., & Short, A. J. (2007, Oct). Efficient classical simulation of the approximate quantum Fourier transform. Physical Review A, 76, 042321.Google Scholar
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