Experimental demonstration of topological error correction

Experimental demonstration of topological error correction


Play all audios:


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. Access through your institution Buy or subscribe


This is a preview of subscription content, access via your institution ACCESS OPTIONS Access through your institution Subscribe to this journal Receive 51 print issues and online access


$199.00 per year only $3.90 per issue Learn more Buy this article * Purchase on SpringerLink * Instant access to full article PDF Buy now Prices may be subject to local taxes which are


calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS


REMOVING LEAKAGE-INDUCED CORRELATED ERRORS IN SUPERCONDUCTING QUANTUM ERROR CORRECTION Article Open access 19 March 2021 DETERMINISTIC MULTI-MODE GATES ON A SCALABLE PHOTONIC QUANTUM


COMPUTING PLATFORM Article 08 July 2021 ENCODING A MAGIC STATE WITH BEYOND BREAK-EVEN FIDELITY Article Open access 10 January 2024 REFERENCES * Shor, P. W. in _Proc. 35th Annu. Symp.


Foundations Computer Sci._ 124–134 (IEEE, 1994) Book  Google Scholar  * Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. _Phys. Rev. Lett._ 79, 325–328 (1997)


Article  ADS  CAS  Google Scholar  * Feynman, R. P. Simulating physics with computers. _Int. J. Theor. Phys._ 21, 467–488 (1982) Article  MathSciNet  Google Scholar  * Calderbank, A. R.


& Shor, P. W. Good quantum error-correcting codes exist. _Phys. Rev. A_ 54, 1098–1105 (1996) 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  Google Scholar  * Gottesman, D. Theory of fault-tolerant quantum computation. _Phys. Rev. A_ 57, 127–137


(1998) Article  ADS  CAS  Google Scholar  * Knill, E. Quantum computing with realistically noisy devices. _Nature_ 434, 39–44 (2005) Article  ADS  CAS  PubMed  Google Scholar  * Aliferis,


P., Gottesman, D. & Preskill, J. Quantum accuracy threshold for concatenated distance-3 code. _Quantum Inf. Comput._ 6, 97–165 (2006) MathSciNet  MATH  Google Scholar  * Kitaev, A. Y.


Quantum computations: algorithms and error correction. _Russ. Math. Surv._ 52, 1191–1249 (1997) Article  MathSciNet  Google Scholar  * Spedalieri, F. & Roychowdhury, V. P. Latency in


local, two-dimensional, fault-tolerant quantum computing. _Quantum Inf. Comput._ 9, 666–682 (2009) MathSciNet  MATH  Google Scholar  * Dennis, E., Landahl, A., Kitaev, A. & Preskill, J.


Topological quantum memory. _J. Math. Phys._ 43, 4452–4505 (2002) Article  ADS  MathSciNet  Google Scholar  * Raussendorf, R., Harrington, J. & Goyal, K. A fault-tolerant one-way quantum


computer. _Ann. Phys._ 321, 2242–2270 (2006) Article  ADS  MathSciNet  CAS  Google Scholar  * 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) Article  ADS  Google Scholar  * Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high


threshold in two dimensions. _Phys. Rev. Lett._ 98, 190504 (2007) Article  ADS  PubMed  Google Scholar  * Barrett, S. D. & Stace, T. M. Fault tolerant quantum computation with very high


threshold for loss errors. _Phys. Rev. Lett._ 105, 200502 (2010) Article  ADS  PubMed  Google Scholar  * Stock, R. & James, D. F. V. A scalable, high-speed measurement-based quantum


computer using trapped ions. _Phys. Rev. Lett._ 102, 170501 (2009) Article  ADS  PubMed  Google Scholar  * Devitt, S. J. et al. Topological cluster state computation with photons. _N. J.


Phys._ 11, 083032 (2009) Article  Google Scholar  * 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) Article  ADS  MathSciNet  CAS  Google Scholar  * Wilczek, F. _Fractional Statistics and Anyon Superconductivity_ (World Scientific, 1990) Book  Google Scholar  *


Cory, D. G. et al. Experimental quantum error correction. _Phys. Rev. Lett._ 81, 2152–2155 (1998) Article  ADS  CAS  Google Scholar  * Knill, E., Laflamme, R., Martinez, R. &


Negrevergne, C. Benchmarking quantum computers: the five-qubit error correcting code. _Phys. Rev. Lett._ 86, 5811–5814 (2001) Article  ADS  CAS  PubMed  Google Scholar  * Chiaverini, J. et


al. Realization of quantum error correction. _Nature_ 432, 602–605 (2004) Article  ADS  CAS  PubMed  Google Scholar  * Schindler, P. et al. Experimental repetitive quantum error correction.


_Science_ 332, 1059–1061 (2011) Article  ADS  CAS  PubMed  Google Scholar  * Lu, C.-Y. et al. Experimental quantum coding against qubit loss error. _Proc. Natl Acad. Sci. USA_ 105,


11050–11054 (2008) Article  ADS  CAS  PubMed  PubMed Central  Google Scholar  * Aoki, T. et al. Quantum error correction beyond qubits. _Nature Phys._ 5, 541–546 (2009) Article  ADS  CAS 


Google Scholar  * Raussendorf, R. & Briegel, H. J. A one-way quantum computer. _Phys. Rev. Lett._ 86, 5188–5191 (2001) Article  ADS  CAS  PubMed  Google Scholar  * Schlingemann, D. &


Werner, R. F. Quantum error-correcting codes associated with graphs. _Phys. Rev. A_ 65, 012308 (2001) Article  ADS  Google Scholar  * Kitaev, A. Y. Fault-tolerant quantum computation by


anyons. _Ann. Phys._ 303, 2–30 (2003) Article  ADS  MathSciNet  CAS  Google Scholar  * Bombin, H. & Martin-Delgado, M. A. Topological quantum distillation. _Phys. Rev. Lett._ 97, 180501


(2006) Article  ADS  CAS  PubMed  Google Scholar  * Hatcher, A. _Algebraic Topology_ (Cambridge Univ. Press, 2002) MATH  Google Scholar  * Fowler, A. G. & Goyal, K. Topological cluster


state quantum computing. _Quantum Inf. Comput._ 9, 727–738 (2009) MathSciNet  MATH  Google Scholar  * 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) Article  ADS  Google Scholar  * Kiesel, N. et al. Experimental analysis of a four-qubit photon cluster state. _Phys. Rev. Lett._ 95, 210502 (2005) Article  ADS 


PubMed  Google Scholar  * O’Brien, J. L. Optical quantum computing. _Science_ 318, 1567–1570 (2007) Article  ADS  PubMed  Google Scholar  * 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) Article  ADS  PubMed  Google Scholar  * Chen, S. et


al. Deterministic and storable single-photon source based on quantum memory. _Phys. Rev. Lett._ 97, 173004 (2006) Article  ADS  PubMed  Google Scholar  * Kardynał, B. E., Yuan, Z. L. &


Shields, A. J. An avalanche-photodiode-based photon-number-resolving detector. _Nature Phys._ 2, 425–428 (2008) Google Scholar  * Press, D. et al. Complete quantum control of a single


quantum dot spin using ultrafast optical pulses. _Nature_ 456, 218–221 (2008) Article  ADS  CAS  PubMed  Google Scholar  * Hime, T. et al. Solid-state qubits with current-controlled


coupling. _Science_ 314, 1427–1429 (2006) Article  ADS  CAS  PubMed  Google Scholar  * Hensinger, W. K. et al. T-junction ion trap array for two-dimensional ion shuttling, storage, and


manipulation. _Appl. Phys. Lett._ 88, 034101 (2006) Article  ADS  Google Scholar  * Jaksch, D. et al. Entanglement of atoms via cold controlled collisions. _Phys. Rev. Lett._ 82, 1975–1978


(1999) Article  ADS  CAS  Google Scholar  * Benhelm, J., Kirchmair, G. & Roos, C. F. &. Blatt, R. Towards fault-tolerant quantum computing with trapped ions. _Nature Phys._ 4,


463–466 (2008) Article  ADS  CAS  Google Scholar  Download references 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. AUTHOR INFORMATION AUTHORS AND


AFFILIATIONS * National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, Shanghai Branch, University of Science and Technology of China, Shanghai, 201315,


China Xing-Can Yao, Tian-Xiong Wang, Hao-Ze Chen, Wei-Bo Gao, Zeng-Bing Chen, Nai-Le Liu, Chao-Yang Lu, You-Jin Deng, Yu-Ao Chen & Jian-Wei Pan * CQC2T, School of Physics, University of


Melbourne, Victoria, 3010, Australia Austin G. Fowler * Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada, Robert Raussendorf


Authors * Xing-Can Yao View author publications You can also search for this author inPubMed Google Scholar * Tian-Xiong Wang View author publications You can also search for this author


inPubMed Google Scholar * Hao-Ze Chen View author publications You can also search for this author inPubMed Google Scholar * Wei-Bo Gao View author publications You can also search for this


author inPubMed Google Scholar * Austin G. Fowler View author publications You can also search for this author inPubMed Google Scholar * Robert Raussendorf View author publications You can


also search for this author inPubMed Google Scholar * Zeng-Bing Chen View author publications You can also search for this author inPubMed Google Scholar * Nai-Le Liu View author


publications You can also search for this author inPubMed Google Scholar * Chao-Yang Lu View author publications You can also search for this author inPubMed Google Scholar * You-Jin Deng


View author publications You can also search for this author inPubMed Google Scholar * Yu-Ao Chen View author publications You can also search for this author inPubMed Google Scholar *


Jian-Wei Pan View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS 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. CORRESPONDING AUTHORS Correspondence to Yu-Ao Chen or Jian-Wei Pan. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial


interests. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION This file contains Supplementary Text and Data, Supplementary Figures 1-2 with legends and additional references. (PDF 176 kb)


POWERPOINT SLIDES POWERPOINT SLIDE FOR FIG. 1 POWERPOINT SLIDE FOR FIG. 2 POWERPOINT SLIDE FOR FIG. 3 POWERPOINT SLIDE FOR FIG. 4 POWERPOINT SLIDE FOR FIG. 5 POWERPOINT SLIDE FOR FIG. 6


RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE 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 Download citation * Received: 26 October 2011 * Accepted: 07 December 2011 * Published: 22 February 2012 * Issue Date: 23


February 2012 * DOI: https://doi.org/10.1038/nature10770 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this content: Get shareable link Sorry, a shareable


link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative