Letter | Published:

A programmable two-qubit quantum processor in silicon

Nature volume 555, pages 633637 (29 March 2018) | Download Citation


Now that it is possible to achieve measurement and control fidelities for individual quantum bits (qubits) above the threshold for fault tolerance, attention is moving towards the difficult task of scaling up the number of physical qubits to the large numbers that are needed for fault-tolerant quantum computing1,2. In this context, quantum-dot-based spin qubits could have substantial advantages over other types of qubit owing to their potential for all-electrical operation and ability to be integrated at high density onto an industrial platform3,4,5. Initialization, readout and single- and two-qubit gates have been demonstrated in various quantum-dot-based qubit representations6,7,8,9. However, as seen with small-scale demonstrations of quantum computers using other types of qubit10,11,12,13, combining these elements leads to challenges related to qubit crosstalk, state leakage, calibration and control hardware. Here we overcome these challenges by using carefully designed control techniques to demonstrate a programmable two-qubit quantum processor in a silicon device that can perform the Deutsch–Josza algorithm and the Grover search algorithm—canonical examples of quantum algorithms that outperform their classical analogues. We characterize the entanglement in our processor by using quantum-state tomography of Bell states, measuring state fidelities of 85–89 per cent and concurrences of 73–82 per cent. These results pave the way for larger-scale quantum computers that use spins confined to quantum dots.

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  1. 1.

    et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

  2. 2.

    et al. Demonstration of a small programmable quantum computer with atomic qubits. Nature 536, 63–66 (2016)

  3. 3.

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

  4. 4.

    et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 (2016)

  5. 5.

    et al. Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent. npj Quantum Inf. 3, 34 (2017)

  6. 6.

    et al. Demonstration of entanglement of electrostatically coupled singlet-triplet qubits. Science 336, 202–205 (2012)

  7. 7.

    et al. Quantum control and process tomography of a semiconductor quantum dot hybrid qubit. Nature 511, 70–74 (2014)

  8. 8.

    et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015)

  9. 9.

    et al. Self-consistent measurement and state tomography of an exchange-only spin qubit. Nat. Nanotechnol. 8, 654–659 (2013)

  10. 10.

    et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)

  11. 11.

    et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

  12. 12.

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

  13. 13.

    et al. Decoherence-protected quantum gates for a hybrid solid-state spin register. Nature 484, 82–86 (2012)

  14. 14.

    et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nat. Phys. 7, 109–113 (2011)

  15. 15.

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

  16. 16.

    et al. Silicon quantum electronics. Rev. Mod. Phys. 85, 961–1019 (2013)

  17. 17.

    et al. Electron spin coherence exceeding seconds in high-purity silicon. Nat. Mater. 11, 143–147 (2012)

  18. 18.

    et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014)

  19. 19.

    et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nanotechnol. 9, 986–991 (2014)

  20. 20.

    et al. Gate fidelity and coherence of an electron spin in an Si/SiGe quantum dot with micromagnet. Proc. Natl Acad. Sci. USA 113, 11738–11743 (2016)

  21. 21.

    et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2018)

  22. 22.

    et al. Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot. Nat. Nanotechnol. 9, 666–670 (2014)

  23. 23.

    et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004)

  24. 24.

    , , , & Simultaneous spin-charge relaxation in double quantum dots. Phys. Rev. Lett. 110, 196803 (2013)

  25. 25.

    et al. Electrically driven single-electron spin resonance in a slanting Zeeman field. Nat. Phys. 4, 776–779 (2008)

  26. 26.

    et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008)

  27. 27.

    , , & Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

  28. 28.

    , & Efficient controlled-phase gate for single-spin qubits in quantum dots. Phys. Rev. B 83, 121403 (2011)

  29. 29.

    et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018)

  30. 30.

    & Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)

  31. 31.

    Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

  32. 32.

    et al. Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation. Phys. Rev. Lett. 116, 110402 (2016)

  33. 33.

    et al. Noise suppression using symmetric exchange gates in spin qubits. Phys. Rev. Lett. 116, 116801 (2016)

  34. 34.

  35. 35.

  36. 36.

    et al. Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting. Nat. Commun. 4, 2069 (2013)

  37. 37.

    , , & Measurement of qubits. Phys. Rev. A 64, 052312 (2001)

  38. 38.

    , & Hubbard model description of silicon spin qubits: charge stability diagram and tunnel coupling in Si double quantum dots. Phys. Rev. B 83, 235314 (2011)

  39. 39.

    et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. 110, 146804 (2013)

  40. 40.

    et al. Decoherence in a superconducting quantum bit circuit. Phys. Rev. B 72, 134519 (2005)

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This research was sponsored by the Army Research Office (ARO) under grant numbers W911NF-17-1-0274 and W911NF-12-1-0607. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the ARO or the US Government. The US Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein. Development and maintenance of the growth facilities used for fabricating samples is supported by DOE (DE-FG02-03ER46028). We acknowledge the use of facilities supported by NSF through the University of Wisconsin-Madison MRSEC (DMR-1121288). E.K. was supported by a fellowship from the Nakajima Foundation. We acknowledge financial support from the Marie Skłodowska-Curie actions—Nanoscale solid-state spin systems in emerging quantum technologies—Spin-NANO, grant agreement number 676108. We acknowledge discussions with S. Dobrovitski, C. Dickel, A. Rol, J. P. Dehollain, Z. Ramlakhan and members of the Vandersypen group, and technical assistance from R. Schouten, R. Vermeulen, M. Tiggelman, M. Ammerlaan, J. Haanstra, R. Roeleveld and O. Benningshof.

Author information


  1. QuTech and the Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands

    • T. F. Watson
    • , S. G. J. Philips
    • , E. Kawakami
    • , P. Scarlino
    • , M. Veldhorst
    •  & L. M. K. Vandersypen
  2. University of Wisconsin-Madison, Madison, Wisconsin 53706, USA

    • D. R. Ward
    • , D. E. Savage
    • , M. G. Lagally
    • , Mark Friesen
    • , S. N. Coppersmith
    •  & M. A. Eriksson


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T.F.W. performed the experiment with help from E.K. and P.S., T.F.W. and S.G.J.P. analysed the data, S.G.J.P. performed the simulations of the algorithms, T.F.W., S.G.J.P., E.K., P.S., M.V., M.F., S.N.C., M.A.E. and L.M.K.V. contributed to the interpretation of the data and commented on the manuscript, D.R.W. fabricated the device, D.E.S. and M.G.L. grew the Si/SiGe heterostructure, T.F.W. wrote the manuscript (S.G.J.P. wrote parts of Methods) and L.M.K.V. conceived and supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to L. M. K. Vandersypen.

Reviewer Information Nature thanks H. Bluhm and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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