Abstract
Scalable quantum computing can be achieved only if quantum bits are manipulated in a fault-tolerant fashion. Topological error correction—a method that combines topological quantum computation with quantum error correction—has the highest known tolerable error rate for a local architecture. The technique makes use of cluster states with topological properties and requires only nearest-neighbour interactions. Here we report the experimental demonstration of topological error correction with an eight-photon cluster state. We show that a correlation can be protected against a single error on any quantum bit. Also, when all quantum bits are simultaneously subjected to errors with equal probability, the effective error rate can be significantly reduced. Our work demonstrates the viability of topological error correction for fault-tolerant quantum information processing.
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References
Shor, P. W. in Proc. 35th Annu. Symp. Foundations Computer Sci. 124–134 (IEEE, 1994)
Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)
Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)
Calderbank, A. R. & Shor, P. W. Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)
Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)
Gottesman, D. Theory of fault-tolerant quantum computation. Phys. Rev. A 57, 127–137 (1998)
Knill, E. Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005)
Aliferis, P., Gottesman, D. & Preskill, J. Quantum accuracy threshold for concatenated distance-3 code. Quantum Inf. Comput. 6, 97–165 (2006)
Kitaev, A. Y. Quantum computations: algorithms and error correction. Russ. Math. Surv. 52, 1191–1249 (1997)
Spedalieri, F. & Roychowdhury, V. P. Latency in local, two-dimensional, fault-tolerant quantum computing. Quantum Inf. Comput. 9, 666–682 (2009)
Dennis, E., Landahl, A., Kitaev, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002)
Raussendorf, R., Harrington, J. & Goyal, K. A fault-tolerant one-way quantum computer. Ann. Phys. 321, 2242–2270 (2006)
Wang, D. S., Austin, A. G. & Hollenberg, L. C. L. Quantum computing with nearest neighbor interactions and error rates over 1%. Phys. Rev. A 83, 020302(R) (2011)
Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007)
Barrett, S. D. & Stace, T. M. Fault tolerant quantum computation with very high threshold for loss errors. Phys. Rev. Lett. 105, 200502 (2010)
Stock, R. & James, D. F. V. A scalable, high-speed measurement-based quantum computer using trapped ions. Phys. Rev. Lett. 102, 170501 (2009)
Devitt, S. J. et al. Topological cluster state computation with photons. N. J. Phys. 11, 083032 (2009)
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Sarma, S. D. Non-abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008)
Wilczek, F. Fractional Statistics and Anyon Superconductivity (World Scientific, 1990)
Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)
Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C. Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)
Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004)
Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011)
Lu, C.-Y. et al. Experimental quantum coding against qubit loss error. Proc. Natl Acad. Sci. USA 105, 11050–11054 (2008)
Aoki, T. et al. Quantum error correction beyond qubits. Nature Phys. 5, 541–546 (2009)
Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)
Schlingemann, D. & Werner, R. F. Quantum error-correcting codes associated with graphs. Phys. Rev. A 65, 012308 (2001)
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003)
Bombin, H. & Martin-Delgado, M. A. Topological quantum distillation. Phys. Rev. Lett. 97, 180501 (2006)
Hatcher, A. Algebraic Topology (Cambridge Univ. Press, 2002)
Fowler, A. G. & Goyal, K. Topological cluster state quantum computing. Quantum Inf. Comput. 9, 727–738 (2009)
Yao, X.-C. et al. Observation of eight-photon entanglement. Nature Photon. (in the press); preprint at 〈http://arxiv.org/abs/1105.6318〉 (2011)
Hofmann, H. F. & Takeuchi, S. Quantum phase gate for photonic qubits using only beam splitters and postselection. Phys. Rev. A 66, 024308 (2002)
Kiesel, N. et al. Experimental analysis of a four-qubit photon cluster state. Phys. Rev. Lett. 95, 210502 (2005)
O’Brien, J. L. Optical quantum computing. Science 318, 1567–1570 (2007)
Varnava, M., Browne, D. E. & Rudolph, T. How good must single photon sources and detectors be for efficient linear optical quantum computation? Phys. Rev. Lett. 100, 060502 (2008)
Chen, S. et al. Deterministic and storable single-photon source based on quantum memory. Phys. Rev. Lett. 97, 173004 (2006)
Kardynał, B. E., Yuan, Z. L. & Shields, A. J. An avalanche-photodiode-based photon-number-resolving detector. Nature Phys. 2, 425–428 (2008)
Press, D. et al. Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456, 218–221 (2008)
Hime, T. et al. Solid-state qubits with current-controlled coupling. Science 314, 1427–1429 (2006)
Hensinger, W. K. et al. T-junction ion trap array for two-dimensional ion shuttling, storage, and manipulation. Appl. Phys. Lett. 88, 034101 (2006)
Jaksch, D. et al. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999)
Benhelm, J., Kirchmair, G. & Roos, C. F. &. Blatt, R. Towards fault-tolerant quantum computing with trapped ions. Nature Phys. 4, 463–466 (2008)
Acknowledgements
We acknowledge discussions with M. A. Martin-Delgado and O. Gühne. We are grateful to X.-H. Bao for his original idea of the ultrabright entanglement and to C.-Z. Peng for his idea of reducing high-order emission. We would also like to thank C. Liu and S. Fölling for their help in designing the figures. This work has been supported by the NNSF of China, the CAS, the National Fundamental Research Program (under grant no. 2011CB921300) and NSERC.
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W.-B.G., A.G.F., R.R., Z.-B.C., Y.-J.D. and J.-W.P. had the idea for and initiated the experiment. A.G.F., R.R. and Y.-J.D. contributed to the general theoretical work. X.-C.Y., C.-Y.L., Y.-A.C. and J.-W.P. designed the experiment. X.-C.Y., T.-X.W. and H.-Z.C. carried out the experiment. X.-C.Y. and Y.-A.C. analysed the data. X.-C.Y., A.G.F., R.R., N.-L.L., C.-Y.L., Y.-J.D., Y.-A.C. and J.-W.P. wrote the manuscript. N.-L.L., Y.-A.C. and J.-W.P. supervised the whole project.
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Yao, XC., Wang, TX., Chen, HZ. et al. Experimental demonstration of topological error correction. Nature 482, 489–494 (2012). https://doi.org/10.1038/nature10770
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DOI: https://doi.org/10.1038/nature10770
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