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Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins

Nature Physics volume 1, pages 177–183 (2005)Cite this article

Abstract

Information processing using quantum systems provides new paradigms for computation and communication and may yield insights into our understanding of the limits of quantum mechanics. However, realistic systems are never perfectly isolated from their environment, hence all quantum operations are subject to errors. Realization of a physical system for processing of quantum information that is tolerant of errors is a fundamental problem in quantum science and engineering. Here, we develop an architecture for quantum computation using electrically controlled semiconductor spins by extending the Loss–DiVincenzo scheme and by combining actively protected quantum memory and long-distance coupling mechanisms. Our approach is based on a demonstrated encoding of qubits in long-lived two-electron states, which immunizes qubits against the dominant error from hyperfine interactions. We develop a universal set of quantum gates compatible with active error suppression for these encoded qubits and an effective long-range interaction between the qubits by controlled electron transport. This approach yields a scalable architecture with favourable error thresholds for fault-tolerant operation, consistent with present experimental parameters.

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Figure 1: Architecture for quantum computation.
Figure 2: Logical qubit.
Figure 3: Long-range qubit transport.
Figure 4: Teleportation-based gates.

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References

  1. Loss, D. & DiVincenzo, D. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  Google Scholar 

  2. Makhlin, Y., Schön, G. & Shnirman, A. Quantum-state engineering with Josephson-junction devices. Rev. Mod. Phys. 73, 357–400 (2001).

    Article  ADS  Google Scholar 

  3. Nakamura, Y., Pashkin, Y. & Tsai, J. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    Article  ADS  Google Scholar 

  4. Chiaverini, J. et al. Implementation of the semiclassical quantum Fourier transform in a scalable system. Science 308, 997–1000 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  5. Cirac, J. I. & Zoller, P. New frontiers in quantum computation with atoms and ions. Phys. Today 57, 38–44 (2004).

    Article  Google Scholar 

  6. Chiorescu, I., Nakamura, Y., Harmans, C. & Mooij, J. Coherent quantum dynamics of a superconducting flux qubit. Science 299, 1869–1871 (2003).

    Article  ADS  Google Scholar 

  7. Heij, C., Dixon, D., van der Wal, C., Hadley, P. & Mooij, J. Quantum superposition of charge states on capacitively coupled superconducting islands. Phys. Rev. B 67, 144512 (2003).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Petta, J. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

    Article  ADS  Google Scholar 

  10. Duan, L.-M. & Guo, G.-C. Preserving coherence in quantum computation by pairing quantum bits. Phys. Rev. Lett. 79, 1953–1956 (1997).

    Article  ADS  Google Scholar 

  11. Zanardi, P. & Rasetti, M. Noiseless quantum codes. Phys. Rev. Lett. 79, 3306–3309 (1997).

    Article  ADS  Google Scholar 

  12. Lidar, D. A., Chuang, I. L. & Whaley, K. B. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998).

    Article  ADS  Google Scholar 

  13. Viola, L., Knill, E. & Lloyd, S. Dynamical generation of noiseless quantum subsystems. Phys. Rev. Lett. 85, 3520–3523 (2000).

    Article  ADS  Google Scholar 

  14. Wu, L.-A. & Lidar, D. A. Creating decoherence-free subspaces using strong and fast pulses. Phys. Rev. Lett. 88, 207902 (2002).

    Article  ADS  Google Scholar 

  15. Levy, J. Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys. Rev. Lett. 89, 147902 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  16. Mohseni, M. & Lidar, D. A. Fault-tolerant quantum computation via exchange interactions. Phys. Rev. Lett. 94, 040507 (2005).

    Article  ADS  Google Scholar 

  17. Taylor, J. M. et al. Solid-state circuit for spin entanglement generation and purification. Phys. Rev. Lett. 94, 236803 (2005).

    Article  ADS  Google Scholar 

  18. Johnson, A. C. et al. Triplet–singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005).

    Article  ADS  Google Scholar 

  19. Bracker, A. S. et al. Optical pumping of electronic and nuclear spin in single charge-tunable quantum dots. Phys. Rev. Lett. 94, 047402 (2005).

    Article  ADS  Google Scholar 

  20. Koppens, F. H. L. et al. Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005).

    Article  ADS  Google Scholar 

  21. Merkulov, I. A., Efros, Al. L. & Rosen, M. Electron spin relaxation by nuclei in semiconductor quantum dots. Phys. Rev. B 65, 205309 (2002).

    Article  ADS  Google Scholar 

  22. Khaetskii, A., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002).

    Article  ADS  Google Scholar 

  23. de Sousa, R. & Das Sarma, S. Electron spin coherence in semiconductors: Considerations for a spin-based solid-state quantum computer architecture. Phys. Rev. B 67, 033301 (2003).

    Article  ADS  Google Scholar 

  24. Steane, A. M. Overhead and noise threshold of fault-tolerant quantum error correction. Phys. Rev. A 68, 042322 (2003).

    Article  ADS  Google Scholar 

  25. Devoret, M. H. & Schoelkopf, R. J. Amplifying quantum signals with the single-electron transistor. Nature 406, 1039–1046 (2000).

    Article  Google Scholar 

  26. Lu, W., Ji, Z., Pfeiffer, L., West, K. W. & Rimberg, A. J. Real-time detection of electron tunnelling in a quantum dot. Nature 423, 422–425 (2003).

    Article  ADS  Google Scholar 

  27. Engel, H.-A. et al. Measurement efficiency and n-shot readout of spin qubits. Phys. Rev. Lett. 93, 106804 (2004).

    Article  ADS  Google Scholar 

  28. Ono, Y., Fujiwara, A., Nishiguchi, K., Inokawa, H. & Takahashi, Y. Manipulation and detection of single electrons for future information processing. J. Appl. Phys. 97, 031101 (2005).

    Article  ADS  Google Scholar 

  29. Kielpinski, D., Monroe, C. & Wineland, D. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002).

    Article  ADS  Google Scholar 

  30. Steane, A. M. Quantum computer architecture for fast entropy extraction. Quant. Inf. Comput. 2, 297–306 (2002).

    MATH  Google Scholar 

  31. Svore, K. M., Terhal, B. M. & DiVincenzo, D. P. Local fault-tolerant quantum computation. Phys. Rev. A 72, 022317 (2005).

    Article  ADS  Google Scholar 

  32. Petta, J. R., Johnson, A. C., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Manipulation of a single charge in a double quantum dot. Phys. Rev. Lett. 93, 186802 (2004).

    Article  ADS  Google Scholar 

  33. Khaetskii, A. V. & Nazarov, Y. V. Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots. Phys. Rev. B 64, 125316 (2001).

    Article  ADS  Google Scholar 

  34. Hanson, R. et al. Zeeman energy and spin relaxation. Phys. Rev. Lett. 91, 196802 (2003).

    Article  ADS  Google Scholar 

  35. Monzon, F. G., Johnson, M. & Roukes, M. L. Strong Hall voltage modulation in hybrid ferromagnetic/semiconductor microstructures. Appl. Phys. Lett. 71, 3087–3089 (1997).

    Article  ADS  Google Scholar 

  36. van der Wiel, W. G. et al. Electron transport through double quantum dots. Rev. Mod. Phys. 75, 1–22 (2003).

    Article  ADS  Google Scholar 

  37. Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995).

    Article  ADS  Google Scholar 

  38. Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–796 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  39. Kikkawa, J. M. & Awschalom, D. D. Lateral drag of spin coherence in gallium arsenide. Nature 397, 139–141 (1999).

    Article  ADS  Google Scholar 

  40. Brandes, T. & Vorrath, T. Adiabatic transfer of electrons in coupled quantum dots. Phys. Rev. B 66, 075341 (2003).

    Article  ADS  Google Scholar 

  41. Barrett, S. D. & Barnes, C. H. W. Double-occupation errors induced by orbital dephasing in exchange-interaction quantum gates. Phys. Rev. B 66, 125318 (2002).

    Article  ADS  Google Scholar 

  42. Hu, X. & Das Sarma, S. Charge fluctuation induced dephasing of exchange coupled spin qubits. Preprint at < http://arxiv.org/abs/cond-mat/0507725> (2005).

  43. Vion, D. et al. Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002).

    Article  ADS  Google Scholar 

  44. Burkard, G., Loss, D. & DiVincenzo, D. P. Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070–2078 (1999).

    Article  ADS  Google Scholar 

  45. Vandersypen, L. M. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2004).

    Article  ADS  Google Scholar 

  46. Gottesman, D. & Chuang, I. L. Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999).

    Article  ADS  Google Scholar 

  47. Zhou, X., Leung, D. W. & Chuang, I. L. Methodology for quantum logic gate constructions. Phys. Rev. A 62, 052316 (2000).

    Article  ADS  Google Scholar 

  48. Knill, E. Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005).

    Article  ADS  Google Scholar 

  49. Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Atom-Photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).

    Google Scholar 

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Acknowledgements

We gratefully acknowledge conversations with J. Folk, A. Houck, A. C. Johnson, D. Loss and especially J. Petta. The work at Harvard was supported by ARO/ARDA, DARPA-QuIST, NSF Career award, NSF grant DMR-02-33773, Alfred P. Sloan Foundation, and David and Lucile Packard Foundation. The work at Innsbruck was supported by the ÖAW through project APART (W.D.), the European Union and the Austrian Science Foundation.

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Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA

    J. M. Taylor, H.-A. Engel, C. M. Marcus & M. D. Lukin

  2. Institute for Theoretical Physics, University of Innsbruck, and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020, Innsbruck, Austria

    W. Dür & P. Zoller

  3. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    A. Yacoby

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  1. J. M. Taylor
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Correspondence to J. M. Taylor.

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Taylor, J., Engel, HA., Dür, W. et al. Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins. Nature Phys 1, 177–183 (2005). https://doi.org/10.1038/nphys174

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