DOI: 10.1038/35023282. Ultimate physical limits to computation

Ultimate physical limits to computation

10.1038/35023282

Crossref journal-article

Springer Science and Business Media LLC

Nature (297)

Bibliography

Lloyd, S. (2000). Ultimate physical limits to computation. Nature, 406(6799), 1047â1054.

Authors 1

Seth Lloyd (first)

References 96 Referenced 759

Maxwell, J. C. Theory of Heat (Appleton, London, 1871). / Theory of Heat by JC Maxwell (1871)
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). (10.1007/BF01341281) / Z. Physik by L Szilard (1929)
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). (10.1147/rd.53.0183) / IBM J. Res. Dev. by R Landauer (1961)
Keyes, R. W. & Landauer, R. Minimal energy dissipation in logic . IBM J. Res. Dev. 14, 152– 157 (1970). (10.1147/rd.142.0152) / IBM J. Res. Dev. by RW Keyes (1970)
Landauer, R. Dissipation and noise-immunity in computation and communication. Nature 335, 779–784 ( 1988). (10.1038/335779a0) / Nature by R Landauer (1988)
Landauer, R. Information is physical. Phys. Today 44, 23–29 (1991). (10.1063/1.881299) / Phys. Today by R Landauer (1991)
Landauer, R. The physical nature of information. Phys. Lett. A 217 , 188–193 (1996). (10.1016/0375-9601(96)00453-7) / Phys. Lett. A by R Landauer (1996)
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). (10.1016/S0019-9958(66)90074-X) / Inform. Control by DS Lebedev (1966)
Levitin, L. B. in Proceedings of the 3rd International Symposium on Radio Electronics part 3, 1–15 (Varna, Bulgaria, 1970). / Proceedings of the 3rd International Symposium on Radio Electronics part 3 by LB Levitin (1970)
Levitin, L. B. Physical limitations of rate, depth, and minimum energy in information processing . Int. J. Theor. Phys. 21, 299– 309 (1982). (10.1007/BF01857732) / Int. J. Theor. Phys. by LB Levitin (1982)
Levitin, L. B. Energy cost of information transmission (along the path to understanding) . Physica D 120, 162–167 (1998). (10.1016/S0167-2789(98)00051-7) / Physica D by LB Levitin (1998)
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). / Proceedings of the Fourth Workshop on Physics and Computation—PhysComp96 by N Margolus (1996)
Margolus, N. & Levitin, L. B. The maximum speed of dynamical evolution. Physica D 120, 188– 195 (1998). (10.1016/S0167-2789(98)00054-2) / Physica D by N Margolus (1998)
Bremermann, H. J. in Self-Organizing Systems (eds Yovits, M. C., Jacobi, G. T. & Goldstein, G. D.) 93–106 (Spartan Books, Washington DC, 1962). / Self-Organizing Systems by HJ Bremermann (1962)
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). / Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability by HJ Bremermann (1967)
Bremermann, H. J. Minimum energy requirements of information transfer and computing. Int. J. Theor. Phys. 21, 203–217 (1982). (10.1007/BF01857726) / Int. J. Theor. Phys. by HJ Bremermann (1982)
Bekenstein, J. D. Universal upper bound on the entropy-to-energy ration for bounded systems . Phys. Rev. D 23, 287– 298 (1981). (10.1103/PhysRevD.23.287) / Phys. Rev. D by JD Bekenstein (1981)
Bekenstein, J. D. Energy cost of information transfer. Phys. Rev. Lett. 46, 623–626 (1981). (10.1103/PhysRevLett.46.623) / Phys. Rev. Lett. by JD Bekenstein (1981)
Bekenstein, J. D. Entropy content and information flow in systems with limited energy. Phys. Rev. D 30, 1669–1679 (1984). (10.1103/PhysRevD.30.1669) / Phys. Rev. D by JD Bekenstein (1984)
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). (10.1103/PhysRev.122.1649) / Phys. Rev. by Y Aharonov (1961)
Aharonov, Y. & Bohm, D. Answer to Fock concerning the time-energy indeterminancy relation. Phys. Rev. B 134, 1417–1418 (1964). (10.1103/PhysRev.134.B1417) / Phys. Rev. B by Y Aharonov (1964)
Anandan, J. & Aharonov, Y. Geometry of quantum evolution. Phys. Rev. Lett. 65, 1697–1700 (1990). (10.1103/PhysRevLett.65.1697) / Phys. Rev. Lett. by J Anandan (1990)
Peres, A. Quantum Theory: Concepts and Methods (Kluwer, Hingham, 1995).
Lecerf, Y. Machines de Turing réversibles. C.R. Acad. Sci. 257, 2597–2600 (1963). / C.R. Acad. Sci. by Y Lecerf (1963)
Bennett, C. H. Logical reversibility of computation. IBM J. Res. Dev. 17, 525–532 (1973). (10.1147/rd.176.0525) / IBM J. Res. Dev. by CH Bennett (1973)
Bennett, C.H. Thermodynamics of computation—a review. Int. J. Theor. Phys. 21, 905–940 ( 1982). (10.1007/BF02084158) / Int. J. Theor. Phys. by CH Bennett (1982)
Bennett, C. H. Demons, engines and the second law. Sci. Am. 257, 108 (1987). (10.1038/scientificamerican1187-108) / Sci. Am. by CH Bennett (1987)
Fredkin, E. & Toffoli, T. Conservative logic. Int. J. Theor. Phys. 21, 219–253 (1982). (10.1007/BF01857727) / Int. J. Theor. Phys. by E Fredkin (1982)
Likharev, K. K. Classical and quantum limitations on energy consumption in computation. Int. J. Theor. Phys. 21, 311–325 (1982). (10.1007/BF01857733) / Int. J. Theor. Phys. by KK Likharev (1982)
Seitz, C. L. et al. in Proceedings of the 1985 Chapel Hill Conference on VLSI (ed. Fuchs, H.) (Computer Science Press, Rockville, MD, 1985). / Proceedings of the 1985 Chapel Hill Conference on VLSI by CL Seitz (1985)
Merkle, R. C. Reversible electronic logic using switches. Nanotechnology 34, 21–40 (1993). (10.1088/0957-4484/4/1/002) / Nanotechnology by RC Merkle (1993)
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). / Proceedings of the 1993 Symposium on Integrated Systems by SG Younis (1993)
Lloyd, S. & Pagels, H. Complexity as thermodynamic depth . Ann. Phys. 188, 186–213 (1988). (10.1016/0003-4916(88)90094-2) / Ann. Phys. by S Lloyd (1988)
Lloyd, S. Use of mutual information to decrease entropy—implications for the Second Law of Thermodynamics. Phys. Rev. A 39, 5378–5386 (1989). (10.1103/PhysRevA.39.5378) / Phys. Rev. A by S Lloyd (1989)
Zurek, W. H. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature 341, 119– 124 (1989). (10.1038/341119a0) / Nature by WH Zurek (1989)
Leff, H. S. & Rex, A. F. Maxwell's Demon: Entropy, Information, Computing (Princeton Univ. Press, Princeton, 1990). (10.1887/0750307595) / Maxwell's Demon: Entropy, Information, Computing by HS Leff (1990)
Lloyd, S. Quantum mechanical Maxwell's demon. Phys. Rev. A 56 , 3374–3382 (1997). (10.1103/PhysRevA.56.3374) / Phys. Rev. A by S Lloyd (1997)
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). (10.1007/BF01011339) / J. Stat. Phys. by P Benioff (1980)
Benioff, P. Quantum mechanical models of Turing machines that dissipate no energy. Phys. Rev. Lett. 48, 1581–1585 (1982). (10.1103/PhysRevLett.48.1581) / Phys. Rev. Lett. by P Benioff (1982)
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982). (10.1007/BF02650179) / Int. J. Theor. Phys. by R Feynman (1982)
Feynman, R. P. Quantum mechanical computers. Optics News 11, 11 (1985); reprinted in Found. Phys. 16, 507 (1986). (10.1364/ON.11.2.000011) / Optics News by RP Feynman (1985)
Zurek, W. H. Reversibility and stability of information-processing systems. Phys. Rev. Lett. 53, 391–394 (1984). (10.1103/PhysRevLett.53.391) / Phys. Rev. Lett. by WH Zurek (1984)
Peres, A. Reversible logic and quantum computers. Phys. Rev. A 32, 3266–3276 (1985). (10.1103/PhysRevA.32.3266) / Phys. Rev. A by A Peres (1985)
Deutsch, D. Quantum-theory, the Church-Turing principle, and the universal quantum computer . Proc. R. Soc. Lond. A 400, 97– 117 (1985). (10.1098/rspa.1985.0070) / Proc. R. Soc. Lond. A by D Deutsch (1985)
Margolus, N. Quantum computation. Ann. N.Y. Acad. Sci. 480, 487–497 (1986). (10.1111/j.1749-6632.1986.tb12451.x) / Ann. N.Y. Acad. Sci. by N Margolus (1986)
Deutsch, D. Quantum computational networks. Proc. R. Soc. Lond. A 425, 73–90 (1989). (10.1098/rspa.1989.0099) / Proc. R. Soc. Lond. A by D Deutsch (1989)
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). / Complexity, Entropy, and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity by N Margolus (1991)
Lloyd, S. Quantum-mechanical computers and uncomputability. Phys. Rev. Lett. 71, 943–946 ( 1993). (10.1103/PhysRevLett.71.943) / Phys. Rev. Lett. by S Lloyd (1993)
Lloyd, S. A potentially realizable quantum computer. Science 261, 1569–1571 (1993). (10.1126/science.261.5128.1569) / Science by S Lloyd (1993)
Lloyd, S. Necessary and sufficient conditions for quantum computation. J. Mod. Opt. 41, 2503–2520 (1994). (10.1080/09500349414552341) / J. Mod. Opt. by S Lloyd (1994)
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). (10.1109/SFCS.1994.365700) / Proceedings of the 35th Annual Symposium on Foundations of Computer Science by P Shor (1994)
Lloyd, S. Quantum-mechanical computers. Sci. Am. 273, 140–145 (1995). (10.1038/scientificamerican1095-140) / Sci. Am. by S Lloyd (1995)
DiVincenzo, D. Quantum computation. Science 270, 255– 261 (1995). (10.1126/science.270.5234.255) / Science by D DiVincenzo (1995)
DiVincenzo, D. P. 2-Bit gates are universal for quantum computation. Phys. Rev. A 51, 1015–1022 ( 1995). (10.1103/PhysRevA.51.1015) / Phys. Rev. A by DP DiVincenzo (1995)
Sleator, T. & Weinfurter, H. Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087– 4090 (1995). (10.1103/PhysRevLett.74.4087) / Phys. Rev. Lett. by T Sleator (1995)
Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 ( 1995). (10.1103/PhysRevA.52.3457) / Phys. Rev. A by A Barenco (1995)
Lloyd, S. Almost any quantum logic gate is universal. Phys. Rev. Lett. 75, 346–349 (1995). (10.1103/PhysRevLett.75.346) / Phys. Rev. Lett. by S Lloyd (1995)
Deutsch, D., Barenco, A. & Ekert, A. Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669–677 (1995). (10.1098/rspa.1995.0065) / Proc. R. Soc. Lond. A by D Deutsch (1995)
Cirac, J. I. & Zoller, P. Quantum computation with cold ion traps. Phys. Rev. Lett. 74, 4091– 4094 (1995). (10.1103/PhysRevLett.74.4091) / Phys. Rev. Lett. by JI Cirac (1995)
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). (10.1103/PhysRevLett.75.3788) / Phys. Rev. Lett. by T Pellizzari (1995)
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). (10.1103/PhysRevLett.75.4710) / Phys. Rev. Lett. by QA Turchette (1995)
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). (10.1103/PhysRevLett.75.4714) / Phys. Rev. Lett. by C Monroe (1995)
Grover, L. K. in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing 212–218 (ACM Press, New York, 1996 ). / Proceedings of the 28th Annual ACM Symposium on the Theory of Computing by LK Grover (1996)
Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996). (10.1126/science.273.5278.1073) / Science by S Lloyd (1996)
Zalka, C. Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond A 454, 313–322 ( 1998). (10.1098/rspa.1998.0162) / Proc. R. Soc. Lond A by C Zalka (1998)
Shor, P. W. A scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, R2493–R2496 ( 1995). (10.1103/PhysRevA.52.R2493) / Phys. Rev. A by PW Shor (1995)
Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996). (10.1103/PhysRevLett.77.793) / Phys. Rev. Lett. by AM Steane (1996)
Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198–201 (1996). (10.1103/PhysRevLett.77.198) / Phys. Rev. Lett. by R Laflamme (1996)
DiVincenzo, D. P. & Shor, P. W. Fault-tolerant error correction with efficient quantum codes. Phys. Rev. Lett. 77, 3260–3263 ( 1996). (10.1103/PhysRevLett.77.3260) / Phys. Rev. Lett. by DP DiVincenzo (1996)
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). / Proceedings of the 37th Annual Symposium on the Foundations of Computer Science by P Shor (1996)
Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454 , 385–410 (1998). (10.1098/rspa.1998.0167) / Proc. R. Soc. Lond. A by J Preskill (1998)
Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 ( 1998). (10.1126/science.279.5349.342) / Science by E Knill (1998)
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). / Proceedings of the Fourth Workshop on Physics and Computation—PhysComp96 by DG Cory (1996)
Gershenfeld, N. A. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350– 356 (1997). (10.1126/science.275.5298.350) / Science by NA Gershenfeld (1997)
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). (10.1038/30181) / Nature by IL Chuang (1998)
Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344– 346 (1998). (10.1038/30687) / Nature by JA Jones (1998)
Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching . Phys. Rev. Lett. 80, 3408– 3411 (1998). (10.1103/PhysRevLett.80.3408) / Phys. Rev. Lett. by IL Chuang (1998)
Kane, B. A silicon-based nuclear-spin quantum computer. Nature 393, 133 (1998). (10.1038/30156) / Nature by B Kane (1998)
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). (10.1038/19718) / Nature by Y Nakamura (1999)
Mooij, J. E. et al. Josephson persistent-current qubit. Science 285, 1036–1039 (1999). (10.1126/science.285.5430.1036) / Science by JE Mooij (1999)
Lloyd, S. & Braunstein, S. Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784– 1787 (1999). (10.1103/PhysRevLett.82.1784) / Phys. Rev. Lett. by S Lloyd (1999)
Abrams, D. & Lloyd, S. Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and P problems. Phys. Rev. Lett. 81, 3992–3995 (1998). (10.1103/PhysRevLett.81.3992) / Phys. Rev. Lett. by D Abrams (1998)
Zel'dovich, Ya. B. & Novikov, I. D. Relativistic Astrophysics (Univ. of Chicago Press, Chicago, 1971 ). / Relativistic Astrophysics by YaB Zel'dovich (1971)
Novikov, I. D. & Frolov, V. P. Black Holes (Springer, Berlin, 1986). / Black Holes by ID Novikov (1986)
Pagels, H. The Cosmic Code: Quantum Physics as the Language of Nature (Simon and Schuster, New York, 1982). / The Cosmic Code: Quantum Physics as the Language of Nature by H Pagels (1982)
Coleman, S., Preskill, J. & Wilczek, F. Growing hair on black-holes. Phys. Rev. Lett. 67, 1975–1978 ( 1991). (10.1103/PhysRevLett.67.1975) / Phys. Rev. Lett. by S Coleman (1991)
Preskill, J. Quantum hair. Phys. Scr. T 36, 258– 264 (1991). (10.1088/0031-8949/1991/T36/028) / Phys. Scr. T by J Preskill (1991)
Fiola, T. M., Preskill, J. & Strominger A. Black-hole thermodynamics and information loss in 2 dimensions. Phys. Rev. D 50, 3987– 4014 (1994). (10.1103/PhysRevD.50.3987) / Phys. Rev. D by TM Fiola (1994)
Susskind, L. & Uglum, J. Black-hole entropy in canonical quantum-gravity and superstring theory. Phys. Rev. D 50, 2700–2711 (1994). (10.1103/PhysRevD.50.2700) / Phys. Rev. D by L Susskind (1994)
Strominger A. & Vafa, C. Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 37, 99– 104 (1996). (10.1016/0370-2693(96)00345-0) / Phys. Lett. B by A Strominger (1996)
Das, S. R. & Mathur, S. D. Comparing decay rates for black holes and D-branes. Nucl. Phys. B 478, 561 –576 (1996). (10.1016/0550-3213(96)00453-1) / Nucl. Phys. B by SR Das (1996)
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). (10.1103/PhysRevD.13.198) / Phys. Rev. D by DN Page (1976)
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). / Black Holes: The Membrane Paradigm Ch. VIII by KS Thorne (1986)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 4:45 a.m.)
Deposited	2 years, 3 months ago (May 16, 2023, 10:06 p.m.)
Indexed	3 days, 14 hours ago (Aug. 23, 2025, 9:09 p.m.)
Issued	25 years ago (Aug. 1, 2000)
Published	25 years ago (Aug. 1, 2000)
Published Print	25 years ago (Aug. 1, 2000)

Funders 0

None

BibTeX

@article{Lloyd_2000, title={Ultimate physical limits to computation}, volume={406}, ISSN={1476-4687}, url={http://dx.doi.org/10.1038/35023282}, DOI={10.1038/35023282}, number={6799}, journal={Nature}, publisher={Springer Science and Business Media LLC}, author={Lloyd, Seth}, year={2000}, month=aug, pages={1047–1054} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        24
      ]
    ],
    "date-time": "2025-08-24T01:09:03Z",
    "timestamp": 1755997743301
  },
  "reference-count": 96,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "6799",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2000,
            8,
            1
          ]
        ],
        "date-time": "2000-08-01T00:00:00Z",
        "timestamp": 965088000000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2000,
        8
      ]
    ]
  },
  "DOI": "10.1038/35023282",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T08:45:49Z",
    "timestamp": 1027673149000
  },
  "page": "1047-1054",
  "source": "Crossref",
  "is-referenced-by-count": 759,
  "title": "Ultimate physical limits to computation",
  "prefix": "10.1038",
  "volume": "406",
  "author": [
    {
      "given": "Seth",
      "family": "Lloyd",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "BF35023282_CR1",
      "volume-title": "Theory of Heat",
      "author": "JC Maxwell",
      "year": "1871",
      "unstructured": "Maxwell, J. C.  Theory of Heat (Appleton, London, 1871)."
    },
    {
      "key": "BF35023282_CR2",
      "unstructured": "Smoluchowski, F.  Vortr\u00e4ge \u00fcber die kinetische Theorie der Materie u. Elektrizitat  (Leipzig, 1914)."
    },
    {
      "key": "BF35023282_CR3",
      "doi-asserted-by": "publisher",
      "first-page": "840",
      "DOI": "10.1007/BF01341281",
      "volume": "53",
      "author": "L Szilard",
      "year": "1929",
      "unstructured": "Szilard, L. \u00dcber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen. Z. Physik 53, 840\u2013 856 (1929).",
      "journal-title": "Z. Physik"
    },
    {
      "key": "BF35023282_CR4",
      "unstructured": "Brillouin, L.  Science and Information Theory (Academic Press, New York, 1953)."
    },
    {
      "key": "BF35023282_CR5",
      "doi-asserted-by": "publisher",
      "first-page": "183",
      "DOI": "10.1147/rd.53.0183",
      "volume": "5",
      "author": "R Landauer",
      "year": "1961",
      "unstructured": "Landauer, R. Irreversibility and heat generation in the computing process.  IBM J. Res. Dev. 5, 183\u2013191 (1961).",
      "journal-title": "IBM J. Res. Dev."
    },
    {
      "key": "BF35023282_CR6",
      "doi-asserted-by": "publisher",
      "first-page": "152",
      "DOI": "10.1147/rd.142.0152",
      "volume": "14",
      "author": "RW Keyes",
      "year": "1970",
      "unstructured": "Keyes, R. W. & Landauer, R. Minimal energy dissipation in logic . IBM J. Res. Dev. 14, 152\u2013 157 (1970).",
      "journal-title": "IBM J. Res. Dev."
    },
    {
      "key": "BF35023282_CR7",
      "doi-asserted-by": "publisher",
      "first-page": "779",
      "DOI": "10.1038/335779a0",
      "volume": "335",
      "author": "R Landauer",
      "year": "1988",
      "unstructured": "Landauer, R. Dissipation and noise-immunity in computation and communication.  Nature 335, 779\u2013784 ( 1988).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR8",
      "doi-asserted-by": "publisher",
      "first-page": "23",
      "DOI": "10.1063/1.881299",
      "volume": "44",
      "author": "R Landauer",
      "year": "1991",
      "unstructured": "Landauer, R. Information is physical. Phys. Today 44, 23\u201329 (1991).",
      "journal-title": "Phys. Today"
    },
    {
      "key": "BF35023282_CR9",
      "doi-asserted-by": "publisher",
      "first-page": "188",
      "DOI": "10.1016/0375-9601(96)00453-7",
      "volume": "217",
      "author": "R Landauer",
      "year": "1996",
      "unstructured": "Landauer, R. The physical nature of information. Phys. Lett. A 217 , 188\u2013193 (1996).",
      "journal-title": "Phys. Lett. A"
    },
    {
      "key": "BF35023282_CR10",
      "unstructured": "von Neumann, J.  Theory of Self-Reproducing Automata Lect. 3 (Univ. Illinois Press, Urbana, IL, 1966)."
    },
    {
      "key": "BF35023282_CR11",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/S0019-9958(66)90074-X",
      "volume": "9",
      "author": "DS Lebedev",
      "year": "1966",
      "unstructured": "Lebedev, D. S. & Levitin, L. B. Information transmission by electromagnetic field. Inform. Control  9, 1\u201322 (1966).",
      "journal-title": "Inform. Control"
    },
    {
      "key": "BF35023282_CR12",
      "first-page": "1",
      "volume-title": "Proceedings of the 3rd International Symposium on Radio Electronics part 3",
      "author": "LB Levitin",
      "year": "1970",
      "unstructured": "Levitin, L. B. in Proceedings of the 3rd International Symposium on Radio Electronics part 3, 1\u201315 (Varna, Bulgaria, 1970)."
    },
    {
      "key": "BF35023282_CR13",
      "doi-asserted-by": "publisher",
      "first-page": "299",
      "DOI": "10.1007/BF01857732",
      "volume": "21",
      "author": "LB Levitin",
      "year": "1982",
      "unstructured": "Levitin, L. B. Physical limitations of rate, depth, and minimum energy in information processing . Int. J. Theor. Phys. 21, 299\u2013 309 (1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR14",
      "doi-asserted-by": "publisher",
      "first-page": "162",
      "DOI": "10.1016/S0167-2789(98)00051-7",
      "volume": "120",
      "author": "LB Levitin",
      "year": "1998",
      "unstructured": "Levitin, L. B. Energy cost of information transmission (along the path to understanding) . Physica D 120, 162\u2013167 (1998).",
      "journal-title": "Physica D"
    },
    {
      "key": "BF35023282_CR15",
      "volume-title": "Proceedings of the Fourth Workshop on Physics and Computation\u2014PhysComp96",
      "author": "N Margolus",
      "year": "1996",
      "unstructured": "Margolus, N. & Levitin, L. B. in Proceedings of the Fourth Workshop on Physics and Computation\u2014PhysComp96 (eds Toffoli, T., Biafore, M. & Le\u00e3o, J.) (New England Complex Systems Institute, Boston, MA, 1996)."
    },
    {
      "key": "BF35023282_CR16",
      "doi-asserted-by": "publisher",
      "first-page": "188",
      "DOI": "10.1016/S0167-2789(98)00054-2",
      "volume": "120",
      "author": "N Margolus",
      "year": "1998",
      "unstructured": "Margolus, N. & Levitin, L. B. The maximum speed of dynamical evolution. Physica D 120, 188\u2013 195 (1998).",
      "journal-title": "Physica D"
    },
    {
      "key": "BF35023282_CR17",
      "first-page": "93",
      "volume-title": "Self-Organizing Systems",
      "author": "HJ Bremermann",
      "year": "1962",
      "unstructured": "Bremermann, H. J. in Self-Organizing Systems (eds Yovits, M. C., Jacobi, G. T. & Goldstein, G. D.) 93\u2013106 (Spartan Books, Washington DC, 1962)."
    },
    {
      "key": "BF35023282_CR18",
      "first-page": "15",
      "volume-title": "Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability",
      "author": "HJ Bremermann",
      "year": "1967",
      "unstructured": "Bremermann, H. J. in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (eds LeCam, L. M. & Neymen, J.) Vol. 4, 15\u201320 (Univ. California Press, Berkeley, CA, 1967)."
    },
    {
      "key": "BF35023282_CR19",
      "doi-asserted-by": "publisher",
      "first-page": "203",
      "DOI": "10.1007/BF01857726",
      "volume": "21",
      "author": "HJ Bremermann",
      "year": "1982",
      "unstructured": "Bremermann, H. J. Minimum energy requirements of information transfer and computing.  Int. J. Theor. Phys. 21, 203\u2013217 (1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR20",
      "doi-asserted-by": "publisher",
      "first-page": "287",
      "DOI": "10.1103/PhysRevD.23.287",
      "volume": "23",
      "author": "JD Bekenstein",
      "year": "1981",
      "unstructured": "Bekenstein, J. D. Universal upper bound on the entropy-to-energy ration for bounded systems . Phys. Rev. D 23, 287\u2013 298 (1981).",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "BF35023282_CR21",
      "doi-asserted-by": "publisher",
      "first-page": "623",
      "DOI": "10.1103/PhysRevLett.46.623",
      "volume": "46",
      "author": "JD Bekenstein",
      "year": "1981",
      "unstructured": "Bekenstein, J. D. Energy cost of information transfer. Phys. Rev. Lett.  46, 623\u2013626 (1981).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR22",
      "doi-asserted-by": "publisher",
      "first-page": "1669",
      "DOI": "10.1103/PhysRevD.30.1669",
      "volume": "30",
      "author": "JD Bekenstein",
      "year": "1984",
      "unstructured": "Bekenstein, J. D. Entropy content and information flow in systems with limited energy.  Phys. Rev. D 30, 1669\u20131679 (1984).",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "BF35023282_CR23",
      "doi-asserted-by": "publisher",
      "first-page": "1649",
      "DOI": "10.1103/PhysRev.122.1649",
      "volume": "122",
      "author": "Y Aharonov",
      "year": "1961",
      "unstructured": "Aharonov, Y. & Bohm, D. Time in the quantum theory and the uncertainty relation for the time and energy domain. Phys. Rev.  122, 1649\u20131658 ( 1961).",
      "journal-title": "Phys. Rev."
    },
    {
      "key": "BF35023282_CR24",
      "doi-asserted-by": "publisher",
      "first-page": "1417",
      "DOI": "10.1103/PhysRev.134.B1417",
      "volume": "134",
      "author": "Y Aharonov",
      "year": "1964",
      "unstructured": "Aharonov, Y. & Bohm, D. Answer to Fock concerning the time-energy indeterminancy relation. Phys. Rev. B 134, 1417\u20131418 (1964).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "BF35023282_CR25",
      "doi-asserted-by": "publisher",
      "first-page": "1697",
      "DOI": "10.1103/PhysRevLett.65.1697",
      "volume": "65",
      "author": "J Anandan",
      "year": "1990",
      "unstructured": "Anandan, J. & Aharonov, Y. Geometry of quantum evolution.  Phys. Rev. Lett. 65, 1697\u20131700 (1990).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR26",
      "unstructured": "Peres, A.  Quantum Theory: Concepts and Methods (Kluwer, Hingham, 1995)."
    },
    {
      "key": "BF35023282_CR27",
      "first-page": "2597",
      "volume": "257",
      "author": "Y Lecerf",
      "year": "1963",
      "unstructured": "Lecerf, Y. Machines de Turing r\u00e9versibles. C.R. Acad. Sci.  257, 2597\u20132600 (1963).",
      "journal-title": "C.R. Acad. Sci."
    },
    {
      "key": "BF35023282_CR28",
      "doi-asserted-by": "publisher",
      "first-page": "525",
      "DOI": "10.1147/rd.176.0525",
      "volume": "17",
      "author": "CH Bennett",
      "year": "1973",
      "unstructured": "Bennett, C. H. Logical reversibility of computation. IBM J. Res. Dev.  17, 525\u2013532 (1973).",
      "journal-title": "IBM J. Res. Dev."
    },
    {
      "key": "BF35023282_CR29",
      "doi-asserted-by": "publisher",
      "first-page": "905",
      "DOI": "10.1007/BF02084158",
      "volume": "21",
      "author": "CH Bennett",
      "year": "1982",
      "unstructured": "Bennett, C.H. Thermodynamics of computation\u2014a review. Int. J. Theor. Phys.  21, 905\u2013940 ( 1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR30",
      "doi-asserted-by": "publisher",
      "first-page": "108",
      "DOI": "10.1038/scientificamerican1187-108",
      "volume": "257",
      "author": "CH Bennett",
      "year": "1987",
      "unstructured": "Bennett, C. H. Demons, engines and the second law. Sci. Am. 257, 108 (1987).",
      "journal-title": "Sci. Am."
    },
    {
      "key": "BF35023282_CR31",
      "doi-asserted-by": "publisher",
      "first-page": "219",
      "DOI": "10.1007/BF01857727",
      "volume": "21",
      "author": "E Fredkin",
      "year": "1982",
      "unstructured": "Fredkin, E. & Toffoli, T. Conservative logic.  Int. J. Theor. Phys. 21, 219\u2013253 (1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR32",
      "doi-asserted-by": "publisher",
      "first-page": "311",
      "DOI": "10.1007/BF01857733",
      "volume": "21",
      "author": "KK Likharev",
      "year": "1982",
      "unstructured": "Likharev, K. K. Classical and quantum limitations on energy consumption in computation.  Int. J. Theor. Phys. 21, 311\u2013325 (1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR33",
      "volume-title": "Proceedings of the 1985 Chapel Hill Conference on VLSI",
      "author": "CL Seitz",
      "year": "1985",
      "unstructured": "Seitz, C. L.  et al. in Proceedings of the 1985 Chapel Hill Conference on VLSI  (ed. Fuchs, H.) (Computer Science Press, Rockville, MD, 1985)."
    },
    {
      "key": "BF35023282_CR34",
      "doi-asserted-by": "publisher",
      "first-page": "21",
      "DOI": "10.1088/0957-4484/4/1/002",
      "volume": "34",
      "author": "RC Merkle",
      "year": "1993",
      "unstructured": "Merkle, R. C. Reversible electronic logic using switches. Nanotechnology  34, 21\u201340 (1993).",
      "journal-title": "Nanotechnology"
    },
    {
      "key": "BF35023282_CR35",
      "volume-title": "Proceedings of the 1993 Symposium on Integrated Systems",
      "author": "SG Younis",
      "year": "1993",
      "unstructured": "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)."
    },
    {
      "key": "BF35023282_CR36",
      "doi-asserted-by": "publisher",
      "first-page": "186",
      "DOI": "10.1016/0003-4916(88)90094-2",
      "volume": "188",
      "author": "S Lloyd",
      "year": "1988",
      "unstructured": "Lloyd, S. & Pagels, H. Complexity as thermodynamic depth . Ann. Phys. 188, 186\u2013213 (1988).",
      "journal-title": "Ann. Phys."
    },
    {
      "key": "BF35023282_CR37",
      "doi-asserted-by": "publisher",
      "first-page": "5378",
      "DOI": "10.1103/PhysRevA.39.5378",
      "volume": "39",
      "author": "S Lloyd",
      "year": "1989",
      "unstructured": "Lloyd, S. Use of mutual information to decrease entropy\u2014implications for the Second Law of Thermodynamics. Phys. Rev. A 39, 5378\u20135386 (1989).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR38",
      "doi-asserted-by": "publisher",
      "first-page": "119",
      "DOI": "10.1038/341119a0",
      "volume": "341",
      "author": "WH Zurek",
      "year": "1989",
      "unstructured": "Zurek, W. H. Thermodynamic cost of computation, algorithmic complexity and the information metric. Nature 341, 119\u2013 124 (1989).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR39",
      "doi-asserted-by": "publisher",
      "DOI": "10.1887/0750307595",
      "volume-title": "Maxwell's Demon: Entropy, Information, Computing",
      "author": "HS Leff",
      "year": "1990",
      "unstructured": "Leff, H. S. & Rex, A. F. Maxwell's Demon: Entropy, Information, Computing (Princeton Univ. Press, Princeton, 1990)."
    },
    {
      "key": "BF35023282_CR40",
      "doi-asserted-by": "publisher",
      "first-page": "3374",
      "DOI": "10.1103/PhysRevA.56.3374",
      "volume": "56",
      "author": "S Lloyd",
      "year": "1997",
      "unstructured": "Lloyd, S. Quantum mechanical Maxwell's demon. Phys. Rev. A 56 , 3374\u20133382 (1997).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR41",
      "doi-asserted-by": "publisher",
      "first-page": "563",
      "DOI": "10.1007/BF01011339",
      "volume": "22",
      "author": "P Benioff",
      "year": "1980",
      "unstructured": "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\u2013591 ( 1980).",
      "journal-title": "J. Stat. Phys."
    },
    {
      "key": "BF35023282_CR42",
      "doi-asserted-by": "publisher",
      "first-page": "1581",
      "DOI": "10.1103/PhysRevLett.48.1581",
      "volume": "48",
      "author": "P Benioff",
      "year": "1982",
      "unstructured": "Benioff, P. Quantum mechanical models of Turing machines that dissipate no energy.  Phys. Rev. Lett. 48, 1581\u20131585 (1982).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR43",
      "doi-asserted-by": "publisher",
      "first-page": "467",
      "DOI": "10.1007/BF02650179",
      "volume": "21",
      "author": "R Feynman",
      "year": "1982",
      "unstructured": "Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys.  21, 467 (1982).",
      "journal-title": "Int. J. Theor. Phys."
    },
    {
      "key": "BF35023282_CR44",
      "doi-asserted-by": "publisher",
      "first-page": "11",
      "DOI": "10.1364/ON.11.2.000011",
      "volume": "11",
      "author": "RP Feynman",
      "year": "1985",
      "unstructured": "Feynman, R. P. Quantum mechanical computers. Optics News 11, 11 (1985); reprinted in Found. Phys.  16, 507 (1986).",
      "journal-title": "Optics News"
    },
    {
      "key": "BF35023282_CR45",
      "doi-asserted-by": "publisher",
      "first-page": "391",
      "DOI": "10.1103/PhysRevLett.53.391",
      "volume": "53",
      "author": "WH Zurek",
      "year": "1984",
      "unstructured": "Zurek, W. H. Reversibility and stability of information-processing systems.  Phys. Rev. Lett. 53, 391\u2013394 (1984).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR46",
      "doi-asserted-by": "publisher",
      "first-page": "3266",
      "DOI": "10.1103/PhysRevA.32.3266",
      "volume": "32",
      "author": "A Peres",
      "year": "1985",
      "unstructured": "Peres, A. Reversible logic and quantum computers. Phys. Rev. A  32, 3266\u20133276 (1985).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR47",
      "doi-asserted-by": "publisher",
      "first-page": "97",
      "DOI": "10.1098/rspa.1985.0070",
      "volume": "400",
      "author": "D Deutsch",
      "year": "1985",
      "unstructured": "Deutsch, D. Quantum-theory, the Church-Turing principle, and the universal quantum computer . Proc. R. Soc. Lond. A 400, 97\u2013 117 (1985).",
      "journal-title": "Proc. R. Soc. Lond. A"
    },
    {
      "key": "BF35023282_CR48",
      "doi-asserted-by": "publisher",
      "first-page": "487",
      "DOI": "10.1111/j.1749-6632.1986.tb12451.x",
      "volume": "480",
      "author": "N Margolus",
      "year": "1986",
      "unstructured": "Margolus, N. Quantum computation. Ann. N.Y. Acad. Sci. 480, 487\u2013497 (1986).",
      "journal-title": "Ann. N.Y. Acad. Sci."
    },
    {
      "key": "BF35023282_CR49",
      "doi-asserted-by": "publisher",
      "first-page": "73",
      "DOI": "10.1098/rspa.1989.0099",
      "volume": "425",
      "author": "D Deutsch",
      "year": "1989",
      "unstructured": "Deutsch, D. Quantum computational networks. Proc. R. Soc. Lond. A  425, 73\u201390 (1989).",
      "journal-title": "Proc. R. Soc. Lond. A"
    },
    {
      "key": "BF35023282_CR50",
      "first-page": "273",
      "volume-title": "Complexity, Entropy, and the Physics of Information, Santa Fe Institute Studies in the Sciences of Complexity",
      "author": "N Margolus",
      "year": "1991",
      "unstructured": "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\u2013288 (Addison Wesley, Redwood City, 1991)."
    },
    {
      "key": "BF35023282_CR51",
      "doi-asserted-by": "publisher",
      "first-page": "943",
      "DOI": "10.1103/PhysRevLett.71.943",
      "volume": "71",
      "author": "S Lloyd",
      "year": "1993",
      "unstructured": "Lloyd, S. Quantum-mechanical computers and uncomputability. Phys. Rev. Lett.  71, 943\u2013946 ( 1993).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR52",
      "doi-asserted-by": "publisher",
      "first-page": "1569",
      "DOI": "10.1126/science.261.5128.1569",
      "volume": "261",
      "author": "S Lloyd",
      "year": "1993",
      "unstructured": "Lloyd, S. A potentially realizable quantum computer. Science  261, 1569\u20131571 (1993).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR53",
      "doi-asserted-by": "publisher",
      "first-page": "2503",
      "DOI": "10.1080/09500349414552341",
      "volume": "41",
      "author": "S Lloyd",
      "year": "1994",
      "unstructured": "Lloyd, S. Necessary and sufficient conditions for quantum computation. J. Mod. Opt. 41, 2503\u20132520 (1994).",
      "journal-title": "J. Mod. Opt."
    },
    {
      "key": "BF35023282_CR54",
      "doi-asserted-by": "publisher",
      "first-page": "124",
      "DOI": "10.1109/SFCS.1994.365700",
      "volume-title": "Proceedings of the 35th Annual Symposium on Foundations of Computer Science",
      "author": "P Shor",
      "year": "1994",
      "unstructured": "Shor, P. in  Proceedings of the 35th Annual Symposium on Foundations of Computer Science  (ed. Goldwasser, S.) 124\u2013134 (IEEE Computer Society, Los Alamitos, CA, 1994)."
    },
    {
      "key": "BF35023282_CR55",
      "doi-asserted-by": "publisher",
      "first-page": "140",
      "DOI": "10.1038/scientificamerican1095-140",
      "volume": "273",
      "author": "S Lloyd",
      "year": "1995",
      "unstructured": "Lloyd, S. Quantum-mechanical computers. Sci. Am. 273, 140\u2013145 (1995).",
      "journal-title": "Sci. Am."
    },
    {
      "key": "BF35023282_CR56",
      "doi-asserted-by": "publisher",
      "first-page": "255",
      "DOI": "10.1126/science.270.5234.255",
      "volume": "270",
      "author": "D DiVincenzo",
      "year": "1995",
      "unstructured": "DiVincenzo, D. Quantum computation. Science 270, 255\u2013 261 (1995).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR57",
      "doi-asserted-by": "publisher",
      "first-page": "1015",
      "DOI": "10.1103/PhysRevA.51.1015",
      "volume": "51",
      "author": "DP DiVincenzo",
      "year": "1995",
      "unstructured": "DiVincenzo, D. P. 2-Bit gates are universal for quantum computation. Phys. Rev. A  51, 1015\u20131022 ( 1995).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR58",
      "doi-asserted-by": "publisher",
      "first-page": "4087",
      "DOI": "10.1103/PhysRevLett.74.4087",
      "volume": "74",
      "author": "T Sleator",
      "year": "1995",
      "unstructured": "Sleator, T. & Weinfurter, H. Realizable universal quantum logic gates. Phys. Rev. Lett. 74, 4087\u2013 4090 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR59",
      "doi-asserted-by": "publisher",
      "first-page": "3457",
      "DOI": "10.1103/PhysRevA.52.3457",
      "volume": "52",
      "author": "A Barenco",
      "year": "1995",
      "unstructured": "Barenco, A.  et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457\u20133467 ( 1995).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR60",
      "doi-asserted-by": "publisher",
      "first-page": "346",
      "DOI": "10.1103/PhysRevLett.75.346",
      "volume": "75",
      "author": "S Lloyd",
      "year": "1995",
      "unstructured": "Lloyd, S. Almost any quantum logic gate is universal. Phys. Rev. Lett.  75, 346\u2013349 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR61",
      "doi-asserted-by": "publisher",
      "first-page": "669",
      "DOI": "10.1098/rspa.1995.0065",
      "volume": "449",
      "author": "D Deutsch",
      "year": "1995",
      "unstructured": "Deutsch, D., Barenco, A. & Ekert, A. Universality in quantum computation. Proc. R. Soc. Lond. A 449, 669\u2013677 (1995).",
      "journal-title": "Proc. R. Soc. Lond. A"
    },
    {
      "key": "BF35023282_CR62",
      "doi-asserted-by": "publisher",
      "first-page": "4091",
      "DOI": "10.1103/PhysRevLett.74.4091",
      "volume": "74",
      "author": "JI Cirac",
      "year": "1995",
      "unstructured": "Cirac, J. I. & Zoller, P. Quantum computation with cold ion traps. Phys. Rev. Lett. 74, 4091\u2013 4094 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR63",
      "doi-asserted-by": "publisher",
      "first-page": "3788",
      "DOI": "10.1103/PhysRevLett.75.3788",
      "volume": "75",
      "author": "T Pellizzari",
      "year": "1995",
      "unstructured": "Pellizzari, T., Gardiner, S. A., Cirac, J. I. & Zoller, P. Decoherence, continuous observation, and quantum computing\u2014a cavity QED model. Phys. Rev. Lett. 75, 3788\u2013 3791 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR64",
      "doi-asserted-by": "publisher",
      "first-page": "4710",
      "DOI": "10.1103/PhysRevLett.75.4710",
      "volume": "75",
      "author": "QA Turchette",
      "year": "1995",
      "unstructured": "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\u2013 4713 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR65",
      "doi-asserted-by": "publisher",
      "first-page": "4714",
      "DOI": "10.1103/PhysRevLett.75.4714",
      "volume": "75",
      "author": "C Monroe",
      "year": "1995",
      "unstructured": "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\u20134717 (1995).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR66",
      "first-page": "212",
      "volume-title": "Proceedings of the 28th Annual ACM Symposium on the Theory of Computing",
      "author": "LK Grover",
      "year": "1996",
      "unstructured": "Grover, L. K. in  Proceedings of the 28th Annual ACM Symposium on the Theory of Computing 212\u2013218 (ACM Press, New York, 1996 )."
    },
    {
      "key": "BF35023282_CR67",
      "doi-asserted-by": "publisher",
      "first-page": "1073",
      "DOI": "10.1126/science.273.5278.1073",
      "volume": "273",
      "author": "S Lloyd",
      "year": "1996",
      "unstructured": "Lloyd, S. Universal quantum simulators. Science 273, 1073\u20131078 (1996).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR68",
      "doi-asserted-by": "publisher",
      "first-page": "313",
      "DOI": "10.1098/rspa.1998.0162",
      "volume": "454",
      "author": "C Zalka",
      "year": "1998",
      "unstructured": "Zalka, C. Simulating quantum systems on a quantum computer. Proc. R. Soc. Lond A 454, 313\u2013322 ( 1998).",
      "journal-title": "Proc. R. Soc. Lond A"
    },
    {
      "key": "BF35023282_CR69",
      "doi-asserted-by": "publisher",
      "first-page": "R2493",
      "DOI": "10.1103/PhysRevA.52.R2493",
      "volume": "52",
      "author": "PW Shor",
      "year": "1995",
      "unstructured": "Shor, P. W. A scheme for reducing decoherence in quantum memory. Phys. Rev. A 52, R2493\u2013R2496 ( 1995).",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "BF35023282_CR70",
      "doi-asserted-by": "publisher",
      "first-page": "793",
      "DOI": "10.1103/PhysRevLett.77.793",
      "volume": "77",
      "author": "AM Steane",
      "year": "1996",
      "unstructured": "Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett.  77, 793\u2013797 (1996).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR71",
      "doi-asserted-by": "publisher",
      "first-page": "198",
      "DOI": "10.1103/PhysRevLett.77.198",
      "volume": "77",
      "author": "R Laflamme",
      "year": "1996",
      "unstructured": "Laflamme, R., Miquel, C., Paz, J. P. & Zurek, W. H. Perfect quantum error correcting code. Phys. Rev. Lett. 77, 198\u2013201 (1996).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR72",
      "doi-asserted-by": "publisher",
      "first-page": "3260",
      "DOI": "10.1103/PhysRevLett.77.3260",
      "volume": "77",
      "author": "DP DiVincenzo",
      "year": "1996",
      "unstructured": "DiVincenzo, D. P. & Shor, P. W. Fault-tolerant error correction with efficient quantum codes. Phys. Rev. Lett.  77, 3260\u20133263 ( 1996).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR73",
      "first-page": "56",
      "volume-title": "Proceedings of the 37th Annual Symposium on the Foundations of Computer Science",
      "author": "P Shor",
      "year": "1996",
      "unstructured": "Shor, P. in  Proceedings of the 37th Annual Symposium on the Foundations of Computer Science  56\u201365 (IEEE Computer Society Press, Los Alamitos, CA, 1996)."
    },
    {
      "key": "BF35023282_CR74",
      "doi-asserted-by": "publisher",
      "first-page": "385",
      "DOI": "10.1098/rspa.1998.0167",
      "volume": "454",
      "author": "J Preskill",
      "year": "1998",
      "unstructured": "Preskill, J. Reliable quantum computers. Proc. R. Soc. Lond. A 454 , 385\u2013410 (1998).",
      "journal-title": "Proc. R. Soc. Lond. A"
    },
    {
      "key": "BF35023282_CR75",
      "doi-asserted-by": "publisher",
      "first-page": "342",
      "DOI": "10.1126/science.279.5349.342",
      "volume": "279",
      "author": "E Knill",
      "year": "1998",
      "unstructured": "Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science  279, 342\u2013345 ( 1998).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR76",
      "first-page": "87",
      "volume-title": "Proceedings of the Fourth Workshop on Physics and Computation\u2014PhysComp96",
      "author": "DG Cory",
      "year": "1996",
      "unstructured": "Cory, D. G., Fahmy, A. F. & Havel, T. F. in Proceedings of the Fourth Workshop on Physics and Computation\u2014PhysComp96 (eds Toffoli, T., Biafore, M. & Le\u00e3o, J.) 87\u201391 (New England Complex Systems Institute, Boston, MA, 1996)."
    },
    {
      "key": "BF35023282_CR77",
      "doi-asserted-by": "publisher",
      "first-page": "350",
      "DOI": "10.1126/science.275.5298.350",
      "volume": "275",
      "author": "NA Gershenfeld",
      "year": "1997",
      "unstructured": "Gershenfeld, N. A. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350\u2013 356 (1997).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR78",
      "doi-asserted-by": "publisher",
      "first-page": "143",
      "DOI": "10.1038/30181",
      "volume": "393",
      "author": "IL Chuang",
      "year": "1998",
      "unstructured": "Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143\u2013 146 (1998).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR79",
      "doi-asserted-by": "publisher",
      "first-page": "344",
      "DOI": "10.1038/30687",
      "volume": "393",
      "author": "JA Jones",
      "year": "1998",
      "unstructured": "Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344\u2013 346 (1998).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR80",
      "doi-asserted-by": "publisher",
      "first-page": "3408",
      "DOI": "10.1103/PhysRevLett.80.3408",
      "volume": "80",
      "author": "IL Chuang",
      "year": "1998",
      "unstructured": "Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching . Phys. Rev. Lett. 80, 3408\u2013 3411 (1998).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR81",
      "doi-asserted-by": "publisher",
      "first-page": "133",
      "DOI": "10.1038/30156",
      "volume": "393",
      "author": "B Kane",
      "year": "1998",
      "unstructured": "Kane, B. A silicon-based nuclear-spin quantum computer. Nature  393, 133 (1998).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR82",
      "doi-asserted-by": "publisher",
      "first-page": "786",
      "DOI": "10.1038/19718",
      "volume": "398",
      "author": "Y Nakamura",
      "year": "1999",
      "unstructured": "Nakamura, Y., Pashkin, Yu. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786 \u2013788 (1999).",
      "journal-title": "Nature"
    },
    {
      "key": "BF35023282_CR83",
      "doi-asserted-by": "publisher",
      "first-page": "1036",
      "DOI": "10.1126/science.285.5430.1036",
      "volume": "285",
      "author": "JE Mooij",
      "year": "1999",
      "unstructured": "Mooij, J. E.  et al. Josephson persistent-current qubit. Science  285, 1036\u20131039 (1999).",
      "journal-title": "Science"
    },
    {
      "key": "BF35023282_CR84",
      "doi-asserted-by": "publisher",
      "first-page": "1784",
      "DOI": "10.1103/PhysRevLett.82.1784",
      "volume": "82",
      "author": "S Lloyd",
      "year": "1999",
      "unstructured": "Lloyd, S. & Braunstein, S. Quantum computation over continuous variables. Phys. Rev. Lett. 82, 1784\u2013 1787 (1999).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR85",
      "doi-asserted-by": "publisher",
      "first-page": "3992",
      "DOI": "10.1103/PhysRevLett.81.3992",
      "volume": "81",
      "author": "D Abrams",
      "year": "1998",
      "unstructured": "Abrams, D. & Lloyd, S. Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and P problems. Phys. Rev. Lett. 81, 3992\u20133995 (1998).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR86",
      "volume-title": "Relativistic Astrophysics",
      "author": "YaB Zel'dovich",
      "year": "1971",
      "unstructured": "Zel'dovich, Ya. B. & Novikov, I. D. Relativistic Astrophysics (Univ. of Chicago Press, Chicago, 1971 )."
    },
    {
      "key": "BF35023282_CR87",
      "volume-title": "Black Holes",
      "author": "ID Novikov",
      "year": "1986",
      "unstructured": "Novikov, I. D. & Frolov, V. P. Black Holes  (Springer, Berlin, 1986)."
    },
    {
      "key": "BF35023282_CR88",
      "volume-title": "The Cosmic Code: Quantum Physics as the Language of Nature",
      "author": "H Pagels",
      "year": "1982",
      "unstructured": "Pagels, H.  The Cosmic Code: Quantum Physics as the Language of Nature (Simon and Schuster, New York, 1982)."
    },
    {
      "key": "BF35023282_CR89",
      "doi-asserted-by": "publisher",
      "first-page": "1975",
      "DOI": "10.1103/PhysRevLett.67.1975",
      "volume": "67",
      "author": "S Coleman",
      "year": "1991",
      "unstructured": "Coleman, S., Preskill, J. & Wilczek, F. Growing hair on black-holes. Phys. Rev. Lett.  67, 1975\u20131978 ( 1991).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "BF35023282_CR90",
      "doi-asserted-by": "publisher",
      "first-page": "258",
      "DOI": "10.1088/0031-8949/1991/T36/028",
      "volume": "36",
      "author": "J Preskill",
      "year": "1991",
      "unstructured": "Preskill, J. Quantum hair. Phys. Scr. T 36, 258\u2013 264 (1991).",
      "journal-title": "Phys. Scr. T"
    },
    {
      "key": "BF35023282_CR91",
      "doi-asserted-by": "publisher",
      "first-page": "3987",
      "DOI": "10.1103/PhysRevD.50.3987",
      "volume": "50",
      "author": "TM Fiola",
      "year": "1994",
      "unstructured": "Fiola, T. M., Preskill, J. & Strominger A. Black-hole thermodynamics and information loss in 2 dimensions. Phys. Rev. D 50, 3987\u2013 4014 (1994).",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "BF35023282_CR92",
      "doi-asserted-by": "publisher",
      "first-page": "2700",
      "DOI": "10.1103/PhysRevD.50.2700",
      "volume": "50",
      "author": "L Susskind",
      "year": "1994",
      "unstructured": "Susskind, L. & Uglum, J. Black-hole entropy in canonical quantum-gravity and superstring theory. Phys. Rev. D 50, 2700\u20132711 (1994).",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "BF35023282_CR93",
      "doi-asserted-by": "publisher",
      "first-page": "99",
      "DOI": "10.1016/0370-2693(96)00345-0",
      "volume": "37",
      "author": "A Strominger",
      "year": "1996",
      "unstructured": "Strominger A. & Vafa, C. Microscopic origin of the Bekenstein-Hawking entropy. Phys. Lett. B 37, 99\u2013 104 (1996).",
      "journal-title": "Phys. Lett. B"
    },
    {
      "key": "BF35023282_CR94",
      "doi-asserted-by": "publisher",
      "first-page": "561",
      "DOI": "10.1016/0550-3213(96)00453-1",
      "volume": "478",
      "author": "SR Das",
      "year": "1996",
      "unstructured": "Das, S. R. & Mathur, S. D. Comparing decay rates for black holes and D-branes. Nucl. Phys. B 478, 561 \u2013576 (1996).",
      "journal-title": "Nucl. Phys. B"
    },
    {
      "key": "BF35023282_CR95",
      "doi-asserted-by": "publisher",
      "first-page": "198",
      "DOI": "10.1103/PhysRevD.13.198",
      "volume": "13",
      "author": "DN Page",
      "year": "1976",
      "unstructured": "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).",
      "journal-title": "Phys. Rev. D"
    },
    {
      "key": "BF35023282_CR96",
      "first-page": "280",
      "volume-title": "Black Holes: The Membrane Paradigm Ch. VIII",
      "author": "KS Thorne",
      "year": "1986",
      "unstructured": "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\u2013 340 (Yale Univ. Press, New Haven, CT, 1986)."
    }
  ],
  "container-title": "Nature",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://www.nature.com/articles/35023282.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://www.nature.com/articles/35023282",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://www.nature.com/articles/35023282.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        5,
        17
      ]
    ],
    "date-time": "2023-05-17T02:06:12Z",
    "timestamp": 1684289172000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.nature.com/articles/35023282"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2000,
        8
      ]
    ]
  },
  "references-count": 96,
  "journal-issue": {
    "issue": "6799",
    "published-print": {
      "date-parts": [
        [
          2000,
          8
        ]
      ]
    }
  },
  "alternative-id": [
    "BF35023282"
  ],
  "URL": "http://dx.doi.org/10.1038/35023282",
  "relation": {},
  "ISSN": [
    "0028-0836",
    "1476-4687"
  ],
  "subject": [],
  "container-title-short": "Nature",
  "published": {
    "date-parts": [
      [
        2000,
        8
      ]
    ]
  }
}