Abstract
Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes1. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used2. Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state3,4, induce errors on the qubits and decode the error syndrome—a quantum state indicating which error has occurred—by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 ± 1 per cent fidelity to the expected classical action of this gate, and 78 ± 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times5,6, this could lead to scalable quantum technology.
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References
Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)
Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Ser. Inf. Nat. Sci, Cambridge Univ. Press, 2000)
DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010)
Neeley, M. et al. Generation of three-qubit entangled states using superconducting phase qubits. Nature 467, 570–573 (2010)
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)
Kim, Z. et al. Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms. Phys. Rev. Lett. 106, 120501 (2011)
Cory, D. 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)
Boulant, N., Viola, L., Fortunato, E. & Cory, D. Experimental implementation of a concatenated quantum error-correcting code. Phys. Rev. Lett. 94, 130501 (2005)
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)
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)
Shor, P. W. in Proc. 37th Symp. Foundations Comput.. 56–65 (IEEE, 1996); preprint at 〈http://arxiv.org/abs/quant-ph/9605011〉 (1996)
Reed, M. D. et al. Fast reset and suppressing spontaneous emission of a superconducting qubit. Appl. Phys. Lett. 96, 203110 (2010)
Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Statist. Comput. 26, 1484–1509 (1997)
Lanyon, B. P. et al. Simplifying quantum logic using higher-dimensional Hilbert spaces. Nature Phys. 5, 134–140 (2009)
Monz, T. et al. Realization of the quantum Toffoli gate with trapped ions. Phys. Rev. Lett. 102, 040501 (2009)
Mariantoni, M. et al. Implementing the quantum von Neumann architecture with superconducting circuits. Science 334, 61–65 (2011)
Fedorov, A., Steffen, L., Baur, M. & Wallraff, A. Implementation of a Toffoli gate with superconducting circuits. Nature 481, 170–172 (2012)
Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)
Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502 (2008)
Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)
DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)
Reed, M. et al. High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity. Phys. Rev. Lett. 105, 173601 (2010)
Strauch, F. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003)
Greenberger, D. M., Horne, M. A. & Zeilinger, A. in Bell’s Theorem, Quantum Theory and Conceptions of the Universe (ed. Kafatos, M. ) 69–72 (Kluwer Academic, 1989)
Tornberg, L., Wallquist, M., Johansson, G., Shumeiko, V. & Wendin, G. Implementation of the three-qubit phase-flip error correction code with superconducting qubits. Phys. Rev. B 77, 214528 (2008)
Acknowledgements
We thank G. Kirchmair, M. Mirrahimi, I. Chuang and M. Devoret for discussions. We acknowledge support from LPS/NSA under ARO contract no. W911NF-09-1-0514 and from the NSF under grants no. DMR-0653377 and no. DMR-1004406. Additional support was provided by CNR-Istituto di Cibernetica, Pozzuoli, Italy (L.F.), the Swiss NSF (S.E.N.) and the Dutch NWO (L.D.C.).
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M.D.R. carried out measurements and performed data analysis. L.D.C. designed the three-qubit gate and conducted initial measurements. L.S. provided further experimental contributions. S.E.N. and S.M.G. provided theoretical support. L.F., L.D.C. and L.S. fabricated the devices. M.D.R. wrote the manuscript, with feedback from all authors. S.M.G. and R.J.S. designed and supervised the project.
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Reed, M., DiCarlo, L., Nigg, S. et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012). https://doi.org/10.1038/nature10786
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DOI: https://doi.org/10.1038/nature10786
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