Ultimate physical limits to computation (original) (raw)

• Maxwell, J. C. Theory of Heat (Appleton, London, 1871).
  Google Scholar
• Smoluchowski, F. Vorträge über die kinetische Theorie der Materie u. Elektrizitat (Leipzig, 1914).
• Szilard, L. Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen. Z. Physik 53, 840– 856 (1929).
  Article ADS CAS MATH Google Scholar
• Brillouin, L. Science and Information Theory (Academic Press, New York, 1953).
• Landauer, R. Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191 (1961).
  Article MathSciNet MATH Google Scholar
• Keyes, R. W. & Landauer, R. Minimal energy dissipation in logic . IBM J. Res. Dev. 14, 152– 157 (1970).
  Article Google Scholar
• Landauer, R. Dissipation and noise-immunity in computation and communication. Nature 335, 779–784 ( 1988).
  Article ADS Google Scholar
• Landauer, R. Information is physical. Phys. Today 44, 23–29 (1991).
  Article ADS Google Scholar
• Landauer, R. The physical nature of information. Phys. Lett. A 217 , 188–193 (1996).
  Article ADS MathSciNet CAS MATH Google Scholar
• von Neumann, J. Theory of Self-Reproducing Automata Lect. 3 (Univ. Illinois Press, Urbana, IL, 1966).
• Lebedev, D. S. & Levitin, L. B. Information transmission by electromagnetic field. Inform. Control 9, 1–22 (1966).
  Article Google Scholar
• Levitin, L. B. in Proceedings of the 3rd International Symposium on Radio Electronics part 3, 1–15 (Varna, Bulgaria, 1970).
  Google Scholar
• Levitin, L. B. Physical limitations of rate, depth, and minimum energy in information processing . Int. J. Theor. Phys. 21, 299– 309 (1982).
  Article Google Scholar
• Levitin, L. B. Energy cost of information transmission (along the path to understanding) . Physica D 120, 162–167 (1998).
  Article ADS Google Scholar
• Margolus, N. & Levitin, L. B. in Proceedings of the Fourth Workshop on Physics and Computation—PhysComp96 (eds Toffoli, T., Biafore, M. & Leão, J.) (New England Complex Systems Institute, Boston, MA, 1996).
  Google Scholar
• Margolus, N. & Levitin, L. B. The maximum speed of dynamical evolution. Physica D 120, 188– 195 (1998).
  Article ADS Google Scholar
• Bremermann, H. J. in Self-Organizing Systems (eds Yovits, M. C., Jacobi, G. T. & Goldstein, G. D.) 93–106 (Spartan Books, Washington DC, 1962).
  Google Scholar
• Bremermann, H. J. in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (eds LeCam, L. M. & Neymen, J.) Vol. 4, 15–20 (Univ. California Press, Berkeley, CA, 1967).
  Google Scholar
• Bremermann, H. J. Minimum energy requirements of information transfer and computing. Int. J. Theor. Phys. 21, 203–217 (1982).
  Article MathSciNet MATH Google Scholar
• Bekenstein, J. D. Universal upper bound on the entropy-to-energy ration for bounded systems . Phys. Rev. D 23, 287– 298 (1981).
  Article ADS MathSciNet Google Scholar
• Bekenstein, J. D. Energy cost of information transfer. Phys. Rev. Lett. 46, 623–626 (1981).
  Article ADS MathSciNet Google Scholar
• Bekenstein, J. D. Entropy content and information flow in systems with limited energy. Phys. Rev. D 30, 1669–1679 (1984).
  Article ADS MathSciNet CAS Google Scholar
• Aharonov, Y. & Bohm, D. Time in the quantum theory and the uncertainty relation for the time and energy domain. Phys. Rev. 122, 1649–1658 ( 1961).
  Article ADS MathSciNet MATH Google Scholar
• Aharonov, Y. & Bohm, D. Answer to Fock concerning the time-energy indeterminancy relation. Phys. Rev. B 134, 1417–1418 (1964).
  Article ADS MATH Google Scholar
• Anandan, J. & Aharonov, Y. Geometry of quantum evolution. Phys. Rev. Lett. 65, 1697–1700 (1990).
  Article ADS MathSciNet CAS MATH PubMed Google Scholar
• Peres, A. Quantum Theory: Concepts and Methods (Kluwer, Hingham, 1995).
• Lecerf, Y. Machines de Turing réversibles. C.R. Acad. Sci. 257, 2597–2600 (1963).
  MathSciNet Google Scholar
• Bennett, C. H. Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973).
  Article MathSciNet MATH Google Scholar
• Bennett, C.H. Thermodynamics of computation—a review. Int. J. Theor. Phys. 21, 905–940 ( 1982).
  Article CAS Google Scholar
• Bennett, C. H. Demons, engines and the second law. Sci. Am. 257, 108 (1987).
  Article ADS Google Scholar
• Fredkin, E. & Toffoli, T. Conservative logic. Int. J. Theor. Phys. 21, 219–253 (1982).
  Article MathSciNet MATH Google Scholar
• Likharev, K. K. Classical and quantum limitations on energy consumption in computation. Int. J. Theor. Phys. 21, 311–325 (1982).
  Article Google Scholar
• Seitz, C. L. et al. in Proceedings of the 1985 Chapel Hill Conference on VLSI (ed. Fuchs, H.) (Computer Science Press, Rockville, MD, 1985).
  Google Scholar
• Merkle, R. C. Reversible electronic logic using switches. Nanotechnology 34, 21–40 (1993).
  Article ADS Google Scholar
• Younis, S. G. & Knight, T. F. in Proceedings of the 1993 Symposium on Integrated Systems, Seattle, Washington (eds Berrielo, G. & Ebeling, C.) (MIT Press, Cambridge, MA, 1993).
  Google Scholar
• Lloyd, S. & Pagels, H. Complexity as thermodynamic depth . Ann. Phys. 188, 186–213 (1988).
  Article ADS MathSciNet Google Scholar
• Lloyd, S. Use of mutual information to decrease entropy—implications for the Second Law of Thermodynamics. Phys. Rev. A 39, 5378–5386 (1989).
  Article ADS MathSciNet CAS Google Scholar
• Zurek, W. H. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature 341, 119– 124 (1989).
  Article ADS Google Scholar
• Leff, H. S. & Rex, A. F. Maxwell's Demon: Entropy, Information, Computing (Princeton Univ. Press, Princeton, 1990).
  Book Google Scholar
• Lloyd, S. Quantum mechanical Maxwell's demon. Phys. Rev. A 56 , 3374–3382 (1997).
  Article ADS CAS Google Scholar
• Benioff, P. The computer as a physical system: a microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Stat. Phys. 22, 563–591 ( 1980).
  Article ADS MathSciNet MATH Google Scholar
• Benioff, P. Quantum mechanical models of Turing machines that dissipate no energy. Phys. Rev. Lett. 48, 1581–1585 (1982).
  Article ADS MathSciNet Google Scholar
• Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982).
  Article MathSciNet Google Scholar
• Feynman, R. P. Quantum mechanical computers. Optics News 11, 11 (1985); reprinted in Found. Phys. 16, 507 (1986).
  Article Google Scholar
• Zurek, W. H. Reversibility and stability of information-processing systems. Phys. Rev. Lett. 53, 391–394 (1984).
  Article ADS Google Scholar
• Peres, A. Reversible logic and quantum computers. Phys. Rev. A 32, 3266–3276 (1985).
  Article ADS MathSciNet CAS Google Scholar
• Deutsch, D. Quantum-theory, the Church-Turing principle, and the universal quantum computer . Proc. R. Soc. Lond. A 400, 97– 117 (1985).
  Article ADS MathSciNet MATH Google Scholar
• Margolus, N. Quantum computation. Ann. N.Y. Acad. Sci. 480, 487–497 (1986).
  Article ADS Google Scholar
• Deutsch, D. Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989).
  Article ADS MathSciNet MATH Google Scholar
• Margolus, N. in Complexity, Entropy, and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity Vol. VIII (ed. Zurek, W. H.) 273–288 (Addison Wesley, Redwood City, 1991).
  Google Scholar
• Lloyd, S. Quantum-mechanical computers and uncomputability. Phys. Rev. Lett. 71, 943–946 ( 1993).
  Article ADS CAS PubMed Google Scholar
• Lloyd, S. A potentially realizable quantum computer. Science 261, 1569–1571 (1993).
  Article ADS CAS PubMed Google Scholar
• Lloyd, S. Necessary and sufficient conditions for quantum computation. J. Mod. Opt. 41, 2503–2520 (1994).
  Article ADS MathSciNet MATH Google Scholar
• Shor, P. in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (ed. Goldwasser, S.) 124–134 (IEEE Computer Society, Los Alamitos, CA, 1994).
  Book Google Scholar
• Lloyd, S. Quantum-mechanical computers. Sci. Am. 273, 140–145 (1995).
  Article CAS Google Scholar
• DiVincenzo, D. Quantum computation. Science 270, 255– 261 (1995).
  Article ADS MathSciNet CAS MATH Google Scholar
• DiVincenzo, D. P. 2-Bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 ( 1995).
  Article ADS CAS PubMed Google Scholar
• Sleator, T. & Weinfurter, H. Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087– 4090 (1995).
  Article ADS MathSciNet CAS MATH PubMed Google Scholar
• Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 ( 1995).
  Article ADS CAS PubMed Google Scholar
• Lloyd, S. Almost any quantum logic gate is universal. Phys. Rev. Lett. 75, 346–349 (1995).
  Article ADS CAS PubMed Google Scholar
• Deutsch, D., Barenco, A. & Ekert, A. Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669–677 (1995).
  Article ADS MathSciNet MATH Google Scholar
• Cirac, J. I. & Zoller, P. Quantum computation with cold ion traps. Phys. Rev. Lett. 74, 4091– 4094 (1995).
  Article ADS CAS PubMed Google Scholar
• Pellizzari, T., Gardiner, S. A., Cirac, J. I. & Zoller, P. Decoherence, continuous observation, and quantum computing—a cavity QED model. Phys. Rev. Lett. 75, 3788– 3791 (1995).
  Article ADS CAS PubMed Google Scholar
• Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H. & Kimble, H. J. Measurement of conditional phase-shifts for quantum logic. Phys. Rev. Lett. 75, 4710– 4713 (1995).
  Article ADS MathSciNet CAS PubMed MATH Google Scholar
• Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995).
  Article ADS MathSciNet CAS MATH PubMed Google Scholar
• Grover, L. K. in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing 212–218 (ACM Press, New York, 1996 ).
  Google Scholar
• Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).
  Article ADS MathSciNet CAS PubMed MATH Google Scholar
• Zalka, C. Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond A 454, 313–322 ( 1998).
  Article ADS MATH Google Scholar
• Shor, P. W. A scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, R2493–R2496 ( 1995).
  Article ADS CAS PubMed Google Scholar
• Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996).
  Article ADS MathSciNet CAS PubMed MATH Google Scholar
• Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198–201 (1996).
  Article ADS CAS PubMed Google Scholar
• DiVincenzo, D. P. & Shor, P. W. Fault-tolerant error correction with efficient quantum codes. Phys. Rev. Lett. 77, 3260–3263 ( 1996).
  Article ADS CAS PubMed Google Scholar
• Shor, P. in Proceedings of the 37th Annual Symposium on the Foundations of Computer Science 56–65 (IEEE Computer Society Press, Los Alamitos, CA, 1996).
  Google Scholar
• Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454 , 385–410 (1998).
  Article ADS MATH Google Scholar
• Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 ( 1998).
  Article ADS CAS MATH Google Scholar
• Cory, D. G., Fahmy, A. F. & Havel, T. F. in Proceedings of the Fourth Workshop on Physics and Computation—PhysComp96 (eds Toffoli, T., Biafore, M. & Leão, J.) 87–91 (New England Complex Systems Institute, Boston, MA, 1996).
  Google Scholar
• Gershenfeld, N. A. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350– 356 (1997).
  Article MathSciNet CAS MATH PubMed Google Scholar
• Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143– 146 (1998).
  Article ADS CAS Google Scholar
• Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344– 346 (1998).
  Article ADS Google Scholar
• Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching . Phys. Rev. Lett. 80, 3408– 3411 (1998).
  Article ADS CAS Google Scholar
• Kane, B. A silicon-based nuclear-spin quantum computer. Nature 393, 133 (1998).
  Article ADS CAS Google Scholar
• Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786 –788 (1999).
  Article ADS CAS Google Scholar
• Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999).
  Article CAS PubMed Google Scholar
• Lloyd, S. & Braunstein, S. Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784– 1787 (1999).
  Article ADS MathSciNet CAS MATH Google Scholar
• Abrams, D. & Lloyd, S. Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and P problems. Phys. Rev. Lett. 81, 3992–3995 (1998).
  Article ADS CAS Google Scholar
• Zel'dovich, Ya. B. & Novikov, I. D. Relativistic Astrophysics (Univ. of Chicago Press, Chicago, 1971 ).
  Google Scholar
• Novikov, I. D. & Frolov, V. P. Black Holes (Springer, Berlin, 1986).
  Google Scholar
• Pagels, H. The Cosmic Code: Quantum Physics as the Language of Nature (Simon and Schuster, New York, 1982).
  Google Scholar
• Coleman, S., Preskill, J. & Wilczek, F. Growing hair on black-holes. Phys. Rev. Lett. 67, 1975–1978 ( 1991).
  Article ADS MathSciNet CAS MATH PubMed Google Scholar
• Preskill, J. Quantum hair. Phys. Scr. T 36, 258– 264 (1991).
  Article ADS MathSciNet MATH Google Scholar
• Fiola, T. M., Preskill, J. & Strominger A. Black-hole thermodynamics and information loss in 2 dimensions. Phys. Rev. D 50, 3987– 4014 (1994).
  Article ADS MathSciNet CAS Google Scholar
• Susskind, L. & Uglum, J. Black-hole entropy in canonical quantum-gravity and superstring theory. Phys. Rev. D 50, 2700–2711 (1994).
  Article ADS MathSciNet CAS Google Scholar
• Strominger A. & Vafa, C. Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 37, 99– 104 (1996).
  Article ADS MathSciNet MATH Google Scholar
• Das, S. R. & Mathur, S. D. Comparing decay rates for black holes and D-branes. Nucl. Phys. B 478, 561 –576 (1996).
  Article ADS MathSciNet MATH Google Scholar
• Page, D. N. Particle emision rates from a black-hole: massless particles form an uncharged non-rotating black-hole. Phys. Rev. D 13, 198 (1976).
  Article ADS CAS Google Scholar
• Thorne, K. S., Zurek, W. H. & Price R. H. in Black Holes: The Membrane Paradigm Ch. VIII (eds Thorne, K. S., Price, R. H. & Macdonald, D. A.) 280– 340 (Yale Univ. Press, New Haven, CT, 1986).
  Google Scholar