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Demonstration of two-qubit algorithms with a superconducting quantum processor

Abstract

Quantum computers, which harness the superposition and entanglement of physical states, could outperform their classical counterparts in solving problems with technological impact—such as factoring large numbers and searching databases1,2. A quantum processor executes algorithms by applying a programmable sequence of gates to an initialized register of qubits, which coherently evolves into a final state containing the result of the computation. Building a quantum processor is challenging because of the need to meet simultaneously requirements that are in conflict: state preparation, long coherence times, universal gate operations and qubit readout. Processors based on a few qubits have been demonstrated using nuclear magnetic resonance3,4,5, cold ion trap6,7 and optical8 systems, but a solid-state realization has remained an outstanding challenge. Here we demonstrate a two-qubit superconducting processor and the implementation of the Grover search and Deutsch–Jozsa quantum algorithms1,2. We use a two-qubit interaction, tunable in strength by two orders of magnitude on nanosecond timescales, which is mediated by a cavity bus in a circuit quantum electrodynamics architecture9,10. This interaction allows the generation of highly entangled states with concurrence up to 94 per cent. Although this processor constitutes an important step in quantum computing with integrated circuits, continuing efforts to increase qubit coherence times, gate performance and register size will be required to fulfil the promise of a scalable technology.

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Figure 1: Two-qubit cQED device, and cavity/qubit characterization.
Figure 2: Origin and characterization of the controlled-phase gate.
Figure 3: Entanglement on demand.
Figure 4: Implementation of Grover's search algorithm.

References

  1. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

    MATH  Google Scholar 

  2. Kaye, P., Laflamme, R. & Mosca, M. An Introduction to Quantum Computing (Oxford Univ. Press, 2007)

    MATH  Google Scholar 

  3. Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998)

    ADS  CAS  Article  Google Scholar 

  4. Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998)

    ADS  Article  Google Scholar 

  5. Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408–3411 (1998)

    ADS  CAS  Article  Google Scholar 

  6. Guide, S. et al. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003)

    ADS  Article  Google Scholar 

  7. Brickman, K.-A. et al. Implementation of Grover's quantum search algorithm in a scalable system. Phys. Rev. A 72, 050306(R) (2005)

    ADS  Article  Google Scholar 

  8. Kwiat, P. G., Mitchell, J. R., Schwindt, P. D. D. & White, A. G. Grover's search algorithm: an optical approach. J. Mod. Opt. 47, 257–266 (2000)

    ADS  MathSciNet  Article  Google Scholar 

  9. Blais, A., Huang, R.-S., Wallraff, A., Girvin, S. M. & Schoelkopf, R. J. Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)

    ADS  Article  Google Scholar 

  10. Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004)

    ADS  CAS  Article  Google Scholar 

  11. Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008)

    ADS  CAS  Article  Google Scholar 

  12. Schreier, J. A. et al. Suppressing charge noise decoherence in superconducting charge qubits. Phys. Rev. B 77, 180502(R) (2008)

    ADS  Article  Google Scholar 

  13. Lucero, E. et al. High-fidelity gates in a single Josephson qubit. Phys. Rev. Lett. 100, 247001 (2008)

    ADS  Article  Google Scholar 

  14. Chow, J. M. et al. Randomized benchmarking and process tomography for gate errors in a solid-state qubit. Phys. Rev. Lett. 102, 090502 (2009)

    ADS  CAS  Article  Google Scholar 

  15. Yamamoto, T., Pashkin, Yu. A., Astafiev, O., Nakamura, Y. & Tsai, J. S. Demonstration of conditional gate operation using superconducting charge qubits. Nature 425, 941–944 (2003)

    ADS  CAS  Article  Google Scholar 

  16. Plantenberg, J. H., de Groot, P. C., Harmans, C. J. P. M. & Mooij, J. E. Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits. Nature 447, 836–839 (2007)

    ADS  CAS  Article  Google Scholar 

  17. Niskanen, A. O. et al. Quantum coherent tunable coupling of superconducting qubits. Science 316, 723–726 (2007)

    ADS  CAS  Article  Google Scholar 

  18. Steffen, M. et al. Measurement of the entanglement of two superconducting qubits via state tomography. Science 313, 1423–1425 (2006)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  19. Siddiqi, I. et al. RF-driven Josephson bifurcation amplifier for quantum measurement. Phys. Rev. Lett. 93, 207002 (2004)

    ADS  CAS  Article  Google Scholar 

  20. McDermott, R. et al. Simultaneous state measurement of coupled Josephson phase qubits. Science 307, 1299–1302 (2005)

    ADS  CAS  Article  Google Scholar 

  21. Sillanpää, M. A., Park, J. I. & Simmonds, R. W. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature 449, 438–442 (2007)

    ADS  Article  Google Scholar 

  22. Majer, J. et al. Coupling superconducting qubits via a cavity bus. Nature 449, 443–447 (2007)

    ADS  CAS  Article  Google Scholar 

  23. Schuster, D. I. et al. Resolving photon number states in a superconducting circuit. Nature 445, 515–518 (2007)

    ADS  CAS  Article  Google Scholar 

  24. Filipp, S. et al. Two-qubit state tomography using a joint dispersive read-out. Phys. Rev. Lett. 102, 200402 (2009)

    ADS  CAS  Article  Google Scholar 

  25. Houck, A. A. et al. Controlling the spontaneous emission of a superconducting transmon qubit. Phys. Rev. Lett. 101, 080502 (2008)

    ADS  CAS  Article  Google Scholar 

  26. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007)

    ADS  Article  Google Scholar 

  27. Blais, A. et al. Quantum-information processing with circuit quantum electrodynamics. Phys. Rev. A 75, 032329 (2007)

    ADS  Article  Google Scholar 

  28. Tavis, M. & Cummings, F. W. Exact solution for an N-molecule-radiation-field Hamiltonian. Phys. Rev. 170, 379–384 (1968)

    ADS  Article  Google Scholar 

  29. Strauch, F. W. et al. Quantum logic gates for coupled superconducting phase qubits. Phys. Rev. Lett. 91, 167005 (2003)

    ADS  Article  Google Scholar 

  30. Wootters, W. K. Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)

    ADS  CAS  Article  Google Scholar 

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Acknowledgements

We thank V. Manucharyan and E. Boaknin for experimental contributions, and M. H. Devoret, I. L. Chuang and A. Nunnenkamp for discussions. This work was supported by LPS/NSA under ARO contract W911NF-05-1-0365, and by the NSF under grants DMR-0653377 and DMR-0603369. We acknowledge additional support from CIFAR, MRI, MITACS and NSERC (J.M.G.), NSERC, CIFAR and the Alfred P. Sloan Foundation (A.B.), and from CNR-Istituto di Cibernetica, Pozzuoli, Italy (L.F.).

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Correspondence to R. J. Schoelkopf.

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This file contains Supplementary Data, Supplementary References and Figures S1-S3 with Legends. Supplementary Information was corrected on 01 July 2009. (PDF 353 kb)

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DiCarlo, L., Chow, J., Gambetta, J. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009). https://doi.org/10.1038/nature08121

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