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.
References
31
Referenced
388
-
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) -
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) -
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) -
Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004).
(
10.1038/nature03074
) / Nature by J Chiaverini (2004) -
Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011).
(
10.1126/science.1203329
) / Science by P Schindler (2011) -
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) -
Reed, M. D. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 382–385 (2012).
(
10.1038/nature10786
) - Bravyi, S. & Kitaev, A. Quantum codes on a lattice with boundary. Preprint at http://http://arxiv.org/quant-ph/9811052 (1998).
-
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) -
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) - Gottesman, D. Stabilizer Codes and Quantum Error Correction PhD thesis California Institute of Technology (1997).
-
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) -
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) - Kelly, J. et al. State preservation by repetitive error detection in a superconducting quantum circuit. Preprint at http://arxiv.org/abs/1411.7403 (2014).
-
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
) - Ryan, C. A. et al. Tomography via correlation of noisy measurement records. Preprint at http://arxiv.org/abs/1310.6448 (2013).
-
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) -
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) -
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) -
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) |
@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 }