Crossref journal-article
Springer Science and Business Media LLC
Nature Communications (297)
Abstract

AbstractThe ability to detect and deal with errors when manipulating quantum systems is a fundamental requirement for fault-tolerant quantum computing. Unlike classical bits that are subject to only digital bit-flip errors, quantum bits are susceptible to a much larger spectrum of errors, for which any complete quantum error-correcting code must account. Whilst classical bit-flip detection can be realized via a linear array of qubits, a general fault-tolerant quantum error-correcting code requires extending into a higher-dimensional lattice. Here we present a quantum error detection protocol on a two-by-two planar lattice of superconducting qubits. The protocol detects an arbitrary quantum error on an encoded two-qubit entangled state via quantum non-demolition parity measurements on another pair of error syndrome qubits. This result represents a building block towards larger lattices amenable to fault-tolerant quantum error correction architectures such as the surface code.

Bibliography

Córcoles, A. D., Magesan, E., Srinivasan, S. J., Cross, A. W., Steffen, M., Gambetta, J. M., & Chow, J. M. (2015). Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nature Communications, 6(1).

Authors 7
  1. A.D. Córcoles (first)
  2. Easwar Magesan (additional)
  3. Srikanth J. Srinivasan (additional)
  4. Andrew W. Cross (additional)
  5. M. Steffen (additional)
  6. Jay M. Gambetta (additional)
  7. Jerry M. Chow (additional)
References 31 Referenced 388
  1. Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998). (10.1103/PhysRevLett.81.2152) / Phys. Rev. Lett. by DG Cory (1998)
  2. Zhang, J., Laflamme, R. & Suter, D. Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code. Phys. Rev. Lett. 109, 100503 (2012). (10.1103/PhysRevLett.109.100503) / Phys. Rev. Lett. by J Zhang (2012)
  3. Moussa, O., Baugh, J., Ryan, C. A. & Laflamme, R. Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor. Phys. Rev. Lett. 107, 160501 (2011). (10.1103/PhysRevLett.107.160501) / Phys. Rev. Lett. by O Moussa (2011)
  4. Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004). (10.1038/nature03074) / Nature by J Chiaverini (2004)
  5. Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011). (10.1126/science.1203329) / Science by P Schindler (2011)
  6. Nigg, D. et al. Quantum computations on a topologically encoded qubit. Science 345, 302–305 (2014). (10.1126/science.1253742) / Science by D Nigg (2014)
  7. Reed, M. D. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 382–385 (2012). (10.1038/nature10786)
  8. Bravyi, S. & Kitaev, A. Quantum codes on a lattice with boundary. Preprint at http://http://arxiv.org/quant-ph/9811052 (1998).
  9. Kitaev, A. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (1997). (10.1016/S0003-4916(02)00018-0) / Ann. Phys. by A Kitaev (1997)
  10. Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007). (10.1103/PhysRevLett.98.190504) / Phys. Rev. Lett. by R Raussendorf (2007)
  11. Gottesman, D. Stabilizer Codes and Quantum Error Correction PhD thesis California Institute of Technology (1997).
  12. Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002). (10.1063/1.1499754) / J. Math. Phys. by E Dennis (2002)
  13. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012). (10.1103/PhysRevA.86.032324) / Phys. Rev. A by AG Fowler (2012)
  14. Chow, J. M. et al. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Nat. Commun. 5, 500 (2014). (10.1038/ncomms5015) / Nat. Commun. by JM Chow (2014)
  15. Paik, H. et al. Observation of high coherence in josephson junction qubits measured in a three-dimensional circuit qed architecture. Phys. Rev. Lett. 107, 240501 (2011). (10.1103/PhysRevLett.107.240501) / Phys. Rev. Lett. by H Paik (2011)
  16. Chang, J. B. et al. Improved superconducting qubit coherence using titanium nitride. Appl. Phys. Lett. 103, 012602 (2013). (10.1063/1.4813269) / Appl. Phys. Lett. by JB Chang (2013)
  17. Barends, R. et al. Coherent josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013). (10.1103/PhysRevLett.111.080502) / Phys. Rev. Lett. by R Barends (2013)
  18. Barends, R. et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014). (10.1038/nature13171) / Nature by R Barends (2014)
  19. Shankar, S. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419–422 (2013). (10.1038/nature12802) / Nature by S Shankar (2013)
  20. Johnson, J. E. et al. Heralded state preparation in a superconducting qubit. Phys. Rev. Lett. 109, 050506 (2012). (10.1103/PhysRevLett.109.050506) / Phys. Rev. Lett. by JE Johnson (2012)
  21. Riste, D., van Leeuwen, J. G., Ku, H.-S., Lehnert, K. W. & DiCarlo, L. Initialization by measurement of a superconducting quantum bit circuit. Phys. Rev. Lett. 109, 050507 (2012). (10.1103/PhysRevLett.109.050507) / Phys. Rev. Lett. by D Riste (2012)
  22. Corcoles, A. D. et al. Process verification of two-qubit quantum gates by randomized benchmarking. Phys. Rev. A 87, 030301 (2013). (10.1103/PhysRevA.87.030301) / Phys. Rev. A by AD Corcoles (2013)
  23. Gambetta, J. M. et al. Characterization of addressability by simultaneous randomized benchmarking. Phys. Rev. Lett. 109, 240504 (2012). (10.1103/PhysRevLett.109.240504) / Phys. Rev. Lett. by JM Gambetta (2012)
  24. Saira, O.-P. et al. Entanglement genesis by ancilla-based parity measurement in 2d circuit qed. Phys. Rev. Lett. 112, 070502 (2014). (10.1103/PhysRevLett.112.070502) / Phys. Rev. Lett. by O-P Saira (2014)
  25. Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Preprint at http://arxiv.org/abs/1411.7403 (2014).
  26. Ristè, D. et al. Detecting bit-flip errors in a logical qubit using stabilizer measurements. Preprint at http://arxiv.org/abs/1411.5542 (2014). (10.1038/ncomms7983)
  27. Ryan, C. A. et al. Tomography via correlation of noisy measurement records. Preprint at http://arxiv.org/abs/1310.6448 (2013).
  28. Motzoi, F., Gambetta, J. M., Rebentrost, P. & Wilhelm, F. K. Simple pulses for elimination of leakage in weakly nonlinear qubits. Phys. Rev. Lett. 103, 110501 (2009). (10.1103/PhysRevLett.103.110501) / Phys. Rev. Lett. by F Motzoi (2009)
  29. Chow, J. M. et al. Universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits. Phys. Rev. Lett. 109, 060501 (2012). (10.1103/PhysRevLett.109.060501) / Phys. Rev. Lett. by JM Chow (2012)
  30. Magesan, E., Gambetta, J. M. & Emerson, J. Scalable and robust randomized benchmarking of quantum processes. Phys. Rev. Lett. 106, 180504 (2011). (10.1103/PhysRevLett.106.180504) / Phys. Rev. Lett. by E Magesan (2011)
  31. Smolin, J. A., Gambetta, J. M. & Smith, G. Efficient method for computing the maximum-likelihood quantum state from measurements with additive gaussian noise. Phys. Rev. Lett. 108, 070502 (2012). (10.1103/PhysRevLett.108.070502) / Phys. Rev. Lett. by JA Smolin (2012)
Dates
Type When
Created 10 years, 3 months ago (April 29, 2015, 9:24 a.m.)
Deposited 2 years, 7 months ago (Jan. 5, 2023, 6:43 a.m.)
Indexed 3 days, 11 hours ago (Aug. 22, 2025, 12:53 a.m.)
Issued 10 years, 3 months ago (April 29, 2015)
Published 10 years, 3 months ago (April 29, 2015)
Published Online 10 years, 3 months ago (April 29, 2015)
Funders 0

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@article{C_rcoles_2015, title={Demonstration of a quantum error detection code using a square lattice of four superconducting qubits}, volume={6}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/ncomms7979}, DOI={10.1038/ncomms7979}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Córcoles, A.D. and Magesan, Easwar and Srinivasan, Srikanth J. and Cross, Andrew W. and Steffen, M. and Gambetta, Jay M. and Chow, Jerry M.}, year={2015}, month=apr }