Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-12T20:20:56.731Z Has data issue: false hasContentIssue false
  • English
  • Français

Active Fault-Tolerant Quantum Error Correction: The Curse of the Open System

Published online by Cambridge University Press:  01 January 2022

Amit Hagar
Get access Rights & Permissions [Opens in a new window]

Abstract

Relying on the universality of quantum mechanics and on recent results known as the “threshold theorems,” quantum information scientists deem the question of the feasibility of large-scale, fault-tolerant, and computationally superior quantum computers as purely technological. Reconstructing this question in statistical mechanical terms, this article suggests otherwise by questioning the physical significance of the threshold theorems. The skepticism it advances is neither too strong (hence is consistent with the universality of quantum mechanics) nor too weak (hence is independent of technological contingencies).

Type
Research Article
Information
Philosophy of Science , Volume 76 , Issue 4 , October 2009 , pp. 506 - 535
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

This research is supported by the NSF (Grant SES no. 0847547) and Indiana University's Office of the Vice President for International Affairs. Any opinions, conclusions, or recommendations expressed in this material are mine and do not necessarily reflect the views of the NSF. I thank Itamar Pitowsky for helpful comments and Gerardo Ortiz and Osvaldo Pessoa for discussion. I also thank two anonymous referees for helpful suggestions and comments. I am solely responsible for any mistakes or errors that might appear herein.

References

Aaronson, Scott (2004), “Multilinear Formulas and Skepticism of Quantum Computing”, STOC '04: Proceedings of the Thirty-sixth Annual ACM Symposium on Theory of Computing. New York: Association for Computing Machinery, 118–127.CrossRefGoogle Scholar
Aharonov, Dorit (1998), “Quantum Computation”, in Stauffer, Dietrich (ed.), Annual Reviews of Computational Physics, Vol. 6. Singapore: World Scientific, 259–346.Google Scholar
Aharonov, Dorit, and Ben-Or, Michael (1996), “Fault Tolerant Quantum Computation with Constant Error”, http://arxiv.org/abs/quant-ph/9611025.Google Scholar
Aharonov, Dorit, Ben-Or, Michael, Impagliazzo, Russell, and Nisan, Noam (1996), “Limitations of Noisy Reversible Computation”, http://arxiv.org/abs/quant-ph/9611028v1.Google Scholar
Aharonov, Dorit, Kitaev, Alexei, and Preskill, John (2006), “Fault-Tolerant Quantum Computation with Long-Range Correlated Noise”, Fault-Tolerant Quantum Computation with Long-Range Correlated Noise 96: 050504.Google ScholarPubMed
Alicki, Robert (2004), “Comments on ‘Fault-Tolerant Quantum Computation for Local Non-Markovian Noise’”, http://arxiv.org/abs/quant-ph/0402139v1.Google Scholar
Alicki, Robert (2007) “Comment on ‘Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective’ and ‘Fault-Tolerant Quantum Computation with Long-Range Correlated Noise’”, http://arxiv.org/abs/quant-ph/0702050v1.Google Scholar
Alicki, Robert, and Fannes, Mark (2001), Quantum Dynamical Systems. Oxford: Oxford University Press.CrossRefGoogle Scholar
Alicki, Robert, Horodecky, Michal, Horodecky, Pawel, and Horodecky, Ryszard (2002), “Dynamical Description of Quantum Computing: Generic Nonlocality of Quantum Noise”, Dynamical Description of Quantum Computing: Generic Nonlocality of Quantum Noise A 65: 062101.Google Scholar
Alicki, Robert, Lidar, Daniel, and Zanardi, Paulo (2006), “Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit”, Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit A 73: 052311.Google Scholar
Barenco, Adriano, Berthiaume, Andre, Deutsch, David, Ekert, Artur, Jozsa, Richard, and Macchiavello, Chiara (1996), “Stabilisation of Quantum Computations by Symmetrisation”, http://arxiv.org/abs/quant-ph/9604028.Google Scholar
Bergman, Peter, and Lebowitz, Joel (1955), “New Approach to Non-equilibrium Processes”, New Approach to Non-equilibrium Processes 99 (2): 578–587..Google Scholar
Berry, Michael (1978), “Regular and Irregular Motion”, in Jorna, S. (ed.), Topics in Nonlinear Dynamics. New York: American Institute of Physics, 16–120.Google Scholar
Blatt, J. M. (1959), “An Alternative Approach to the Ergodic Problem”, An Alternative Approach to the Ergodic Problem 22 (6): 745–756..Google Scholar
Boltzmann, Ludwig ([1895] 1964), Lectures on Gas Theory. Reprint. Translated by Steven G. Brush. Berkeley: University of California Press.CrossRefGoogle Scholar
Bonetto, Federico, Lebowitz, Joel, and Rey-Bellet, L. (2000), “Fourier's Law: A Challenge to Theorists”, in Fokas, A., Grigoryan, A., Kibble, T., and Zergarlinski, B. (eds.), Mathematical Physics 2000. London: Imperial College Press, 128–150.CrossRefGoogle Scholar
Borel, Emile (1914), Le Hasard. Paris: Alcan.Google Scholar
Breuer, Heinz-Peter, and Petruccione, Francesco (2003), “Concepts and Methods in the Theory of Open Quantum Systems”, Concepts and Methods in the Theory of Open Quantum Systems 622:65–79.Google Scholar
Brown, Harvey, and Uffink, Jos (2001), “The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law”, The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law 32 (4): 525–538..Google Scholar
Brush, Steven G. (1976), The Kind of Motion We Call Heat. vols. 1–2. Amsterdam: North-Holland.Google Scholar
Bub, Jeff (1997), Interpreting the Quantum World. Cambridge: Cambridge University Press.Google Scholar
Burbury, Samuel H (1895), “Boltzmann's Minimum Function”, Boltzmann's Minimum Function 51: 320.Google Scholar
Davies, Brian E. (1974), “Markovian Master Equations”, Markovian Master Equations 39:91–110.Google Scholar
Davies, Brian E. (1978), “A Model of Heat Conduction”, A Model of Heat Conduction 18:161–170.Google Scholar
Dieks, Dennis (1982), “Communication by Electron-Paramagnetic-Resonance Devices”, Communication by Electron-Paramagnetic-Resonance Devices 92A: 271.Google Scholar
Dyakonov, Michael (2006), “Is Fault-Tolerant Quantum Computation Really Possible?”, http://arxiv.org/abs/quant-ph/0610117.Google Scholar
Dyson, Freeman (2009), “Leaping into the Grand Unknown”, Leaping into the Grand Unknown 56 (6).Google Scholar
Earman, John (1986), “The Problem of Irreversibility”, in Fine, Arthur and Machamer, Peter (eds.), PSA 1986: Proceedings of the 1986 Biennial Meeting of the Philosophy of Science Association, Vol. 2. East Lansing, MI: Philosophy of Science Association, 226–233.Google Scholar
Earman, John, and Redei, Miklos (1996), “Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics”, Why Ergodic Theory Does Not Explain the Success of Equilibrium Statistical Mechanics 47:63–78.Google Scholar
Emerson, Josef, Silva, Marcus, Moussa, Osama, Ryan, Colm, Laforest, Martin, Baugh, Jonathan, Cory, David G., and Laflamme, Raymond (2007), “Symmetrized Characterization of Noisy Quantum Processes”, Symmetrized Characterization of Noisy Quantum Processes 317: 1893.Google ScholarPubMed
Gaitan, Frank (2008), Quantum Error Correction and Fault Tolerant Quantum Computing. Boca Raton, FL: CRC Press.Google Scholar
Gallavotti, Giovanni, and Cohen, E. G. D. (1996), “Dynamical Ensembles and Stationary States”, Dynamical Ensembles and Stationary States 80:931–970.Google Scholar
Gea-Banacloche, Jean (2002), “Minimum Energy Requirements for Quantum Computation”, Minimum Energy Requirements for Quantum Computation 89: 217901.Google ScholarPubMed
Gemmer, J., Michel, M., and Mahler, G. (2004), Quantum Thermodynamics: Lecture Notes in Physics. vol. 657. Berlin: Springer.CrossRefGoogle Scholar
Goldreich, Oded (2005), “On Quantum Computing”, http://www.wisdom.weizmann.ac.il/~oded/on-qc.html.Google Scholar
Goldstein, Shelly, Lebowitz, Joel, Tumulka, Roderich, and Zanghi, Nino (2006), “Canonical Typicality”, Canonical Typicality 96: 050403.Google ScholarPubMed
Gottesman, Danny (1997), “Theory of Fault-Tolerant Quantum Computation”, Theory of Fault-Tolerant Quantum Computation A 57: 127.Google Scholar
Hagar, Amit (2005), “The Foundations of Statistical Mechanics: Questions and Answers”, The Foundations of Statistical Mechanics: Questions and Answers 72:468–478.Google Scholar
Hahn, Erwin (1950), “Spin Echoes”, Spin Echoes 80:580–594.Google Scholar
Haroche, Serge, and Raimond, Jean-Michel (1996), “Quantum Computing: Dream or Nightmare?”, Quantum Computing: Dream or Nightmare? 8:51–52.Google Scholar
Hines, Andrew P., and Stamp, Philip (2007), “Decoherence in Quantum Walks and Quantum Computers”, http://arxiv.org/abs/0711.1555.Google Scholar
Joos, Erich, Zeh, H. Dieter, Kiefer, Claus, Giulini, Domenico, Kupsch, Joachim, and Stamatescu, Ion-Olimpiu (1996), Decoherence and the Appearance of a Classical World in Quantum Theory. Heidelberg: Springer-Verlag.Google Scholar
Kalai, Gil (2005), “Thoughts on Noise and Quantum Computation”, http://arxiv.org/abs/quant-ph/0508095.Google Scholar
Kalai, Gil (2006), “How Quantum Computers Can Fail”, http://arxiv.org/abs/quant-ph/0607021v3.Google Scholar
Kalai, Gil (2008), “Detrimental Decoherence”, http://arxiv.org/abs/0806.2443.Google Scholar
Kalai, Gil (2009), “Quantum Computers: Noise Propagation and Adversarial Noise Models”, http://arxiv.org/abs/0904.3265.Google Scholar
Kastler, Daniel (1978), “Foundations of Equilibrium Quantum Statistical Mechanics”, in Dell'Antonio, G., Doplicher, S., and Jona-Lasinio, G. (eds.), Mathematical Problems in Theoretical Physics. Berlin: Springer, 106–123.CrossRefGoogle Scholar
Kaye, Phillip, Laflamme, Ray, and Mosca, Mike (2007), An Introduction to Quantum Computing. Oxford: Oxford University Press.Google Scholar
Kempe, Julia (2005), “Approaches to Quantum Error Correction”, Approaches to Quantum Error Correction 2:1–29.Google Scholar
Khoon Ng, Hui, and Preskill, John (2008), “Fault-Tolerant Quantum Computation versus Gaussian Noise”, http://arxiv.org/abs/0810.4953.Google Scholar
Knill, Emanuel (2005), “Quantum Computing with Realistically Noisy Devices”, Quantum Computing with Realistically Noisy Devices 434:39–44.Google ScholarPubMed
Knill, Emanuel (2006), “On Protected Realizations of Quantum Information”, http://arxiv.org/abs/quant-ph/0603252.Google Scholar
Knill, Emanuel, and Laflamme, Ray (1996), “Concatenated Quantum Codes”, http://arxiv.org/abs/quant-ph/9608012.Google Scholar
Knill, Emanuel, Laflamme, Ray, and Zurek, Wojciech (1996), “Accuracy Threshold for Quantum Computation”, http://arxiv.org/abs/quant-ph/9610011.Google Scholar
Knill, Emanuel, Laflamme, Ray, and Zurek, Wojciech (1998), “Resilient Quantum Computation: Error-Models and Thresholds”, Resilient Quantum Computation: Error-Models and Thresholds 279:342–345.Google Scholar
Kolmogorov, Andrey (1965), “Three Approaches to the Quantitative Definition of Information”, Three Approaches to the Quantitative Definition of Information 1 (1): 1–7..Google Scholar
Laflamme, Ray, Miquel, Cesar, Paz, Juan Pablo, and Zurek, Wojciech (1996), “Perfect Quantum Error Correction Code”, Perfect Quantum Error Correction Code 77: 198.Google Scholar
Landauer, Rolf (1995), “Is Quantum Mechanics Useful?”, Is Quantum Mechanics Useful? 1703 (353): 367–376..Google Scholar
Lanford, O. (1981), “The Hard Sphere Gas in the Boltzmann-Grad Limit”, The Hard Sphere Gas in the Boltzmann-Grad Limit A 106:70–76.Google Scholar
Lebowitz, Joel (1978), “Exact Results in Non-equilibrium Statistical Mechanics: Where Do We Stand?”, Progress in Theoretical Physics (Suppl.) 64:35–49.CrossRefGoogle Scholar
Lenstra, A. K., and Lenstra, H. W. Jr. (1990), “Algorithms in Number Theory”, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, vol. A, Algorithms and Complexity. Amsterdam: Elsevier, 673–715.Google Scholar
Levin, Leonid (2003), “The Tale of One-Way Functions”, The Tale of One-Way Functions 39:92–103.Google Scholar
Lindblad, Goran (1976), “On the Generators of Quantum Dynamical Semigroups”, On the Generators of Quantum Dynamical Semigroups 48:119–130.Google Scholar
MacWilliams, F. J., and Sloane, N. J. A. (1977), The Theory of Error-Correcting Codes. New York: North-Holland.Google Scholar
Margolus, Norman, and Levitin, Lev (1998), “The Maximum Speed of Dynamical Evolution”, The Maximum Speed of Dynamical Evolution D 120:188–195.Google Scholar
Mermin, David (2007), Quantum Computer Science: An Introduction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Nielsen, Michael, and Chuang, Isaac (2000), Quantum Computation and Quantum Information. Cambridge: Cambridge University Press.Google Scholar
Popescu, Sandu, Short, Anthony J., and Winter, Andreas (2006), “Entanglement and the Foundations of Statistical Mechanics”, Entanglement and the Foundations of Statistical Mechanics 2:754–758.Google Scholar
Preskill, John (1998), “Reliable Quantum Computers”, Reliable Quantum Computers A 454:385–410.Google Scholar
Preskill, John (2007), “Fault-Tolerant Quantum Computation against Realistic Noise”. Talk given at the First International Conference on Quantum Error Correction, University of Southern California, December, http://qserver.usc.edu/qec07/QEC07/JohnPreskill.pdf.Google Scholar
Price, Huw (2003), “Burbury's Last Case: The Mystery of the Entropic Arrow”, in Callender, Craig (ed.) Time, Reality and Experience. Cambridge: Cambridge University Press, 19–56.Google Scholar
Ridderboss, Katinka, and Redhead, Michael (1998), “The Spin Echo Experiments and the Second Law of Thermodynamics”, The Spin Echo Experiments and the Second Law of Thermodynamics 28 (8): 1237–1270..Google Scholar
Rivest, Ronald, Shamir, Adi, and Adleman, Leonid (1978), “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems”, A Method for Obtaining Digital Signatures and Public-Key Cryptosystems 21 (2): 120–126..Google Scholar
Rovelli, Carlo (1994), “Comment on Protective Measurement”, Comment on Protective Measurement A 50:2788–2793.Google Scholar
Santayana, George (1905), The Life of Reason; or, The Phases of Human Progress, Vol. 1, Reason in Common Sense. New York: Scribner's.Google Scholar
Shenker, Orly (2000), “Interventionism in Statistical Mechanics—Some Philosophical Remarks”, University of Pittsburgh PhilSci Archive, http://philsci-archive.pitt.edu/archive/00000151.Google Scholar
Shor, Peter (1994), “Algorithms for Quantum Computation: Discrete Log and Factoring”, in Goldwasser, S. (ed.), Proceedings of the 35th IEEE Symposium on Foundations of Computer Science. Los Alamitos, CA: IEEE Computer Society, 124–134.Google Scholar
Shor, Peter (1995), “Scheme for Reducing Decoherence in Quantum Computer Memory”, Scheme for Reducing Decoherence in Quantum Computer Memory A 52:2493–2496.Google ScholarPubMed
Shor, Peter (1996), “Fault-Tolerant Quantum Computation”, http://arxiv.org/abs/quantph/9605011.Google Scholar
Simon, Daniel R. (1994), “On the Power of Quantum Computation”, in Goldwasser, S. (ed.), Proceedings of the 35th Symposium on Foundations of Computer Science. Los Alamitos, CA: IEEE Computer Society, 116–123.Google Scholar
Steane, Andrew (1996), “Error Correcting Codes in Quantum Theory”, Error Correcting Codes in Quantum Theory 77: 793.Google ScholarPubMed
Tasaki, Hal (1998), “From Quantum Dynamics to Canonical Distribution: General Picture and Rigorous Example”, From Quantum Dynamics to Canonical Distribution: General Picture and Rigorous Example 80:1373–1376.Google Scholar
Terhal, Barbara, and Burkard, Guido (2005), “Fault-Tolerant Quantum Computation for Local Non-Markovian Noise”, Fault-Tolerant Quantum Computation for Local Non-Markovian Noise A 71: 012336.Google Scholar
Uffink, Jos (2001), “Bluff Your Way in the Second Law of Thermodynamics”, Bluff Your Way in the Second Law of Thermodynamics 32:305–394.Google Scholar
Unruh, William (1995), “Maintaining Coherence in Quantum Computers”, Maintaining Coherence in Quantum Computers A 51:992–997.Google ScholarPubMed
von Neumann, John (1956), “Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components”, in Ashby, W. Ross, McCarthy, J. and Shannon, C E. (eds.) Automata Studies. Princeton, NJ: Princeton University Press, 43–98.Google Scholar
Wolfram, Stephen (2001), A New Kind of Science. Champaign, IL: Wolfram Media.Google Scholar
Wootters, William, and Zurek, Wojciech (1982), “Single Quantum Cannot Be Cloned”, Single Quantum Cannot Be Cloned 299: 802.Google Scholar
Zanardi, Paulo, and Rasetti, Mario (1997), “Noiseless Quantum Codes”, Noiseless Quantum Codes 79: 3306.Google Scholar