Storing quantum information for 30 seconds in a nanoelectronic device

Journal name:
Nature Nanotechnology
Volume:
9,
Pages:
986–991
Year published:
DOI:
doi:10.1038/nnano.2014.211
Received
Accepted
Published online

The spin of an electron or a nucleus in a semiconductor1 naturally implements the unit of quantum information—the qubit. In addition, because semiconductors are currently used in the electronics industry, developing qubits in semiconductors would be a promising route to realize scalable quantum information devices2. The solid-state environment, however, may provide deleterious interactions between the qubit and the nuclear spins of surrounding atoms3, or charge and spin fluctuations arising from defects in oxides and interfaces4. For materials such as silicon, enrichment of the spin-zero 28Si isotope drastically reduces spin-bath decoherence5. Experiments on bulk spin ensembles in 28Si crystals have indeed demonstrated extraordinary coherence times6, 7, 8. However, it remained unclear whether these would persist at the single-spin level, in gated nanostructures near amorphous interfaces. Here, we present the coherent operation of individual 31P electron and nuclear spin qubits in a top-gated nanostructure, fabricated on an isotopically engineered 28Si substrate. The 31P nuclear spin sets the new benchmark coherence time (>30 s with Carr–Purcell–Meiboom–Gill (CPMG) sequence) of any single qubit in the solid state and reaches >99.99% control fidelity. The electron spin CPMG coherence time exceeds 0.5 s, and detailed noise spectroscopy9 indicates that—contrary to widespread belief—it is not limited by the proximity to an interface. Instead, decoherence is probably dominated by thermal and magnetic noise external to the device, and is thus amenable to further improvement.

At a glance

Figures

  1. Device structure and the energy states of the electron and nuclear spin qubits.
    Figure 1: Device structure and the energy states of the electron and nuclear spin qubits.

    a, Scanning electron micrograph image of a device similar to device A, highlighting the position of the P donor, the microwave (MW) antenna and the SET for spin readout. b, Schematic of the Si substrate, consisting of an isotopically purified 28Si epilayer (with a residual 29Si concentration of 800 ppm) on top of a natural Si wafer. c, Energy level diagram of the coupled e31P0 system (left) and the ionized 31P+ nucleus (right). Arbitrary quantum states are encoded on the qubits by applying pulses of oscillating magnetic field B1 at the frequencies corresponding to the ESR (νe1,2 ≈ γeB0 ∓ A/2) and NMR (νn1,2 ≈ A/2 ± γnB0), where γe = 27.97 GHz T−1 and γn = 17.23 MHz T−1 are the electron and nuclear gyromagnetic ratios, respectively. The 31P qubit in the ionized state is operated at frequency νn0 = γnB0.

  2. Electron spin qubit.
    Figure 2: Electron spin qubit.

    a, Long-lasting Rabi oscillations of the e qubit. b, e Ramsey fringes, showing a Gaussian decay envelope. c, ESR spectrum. The fit is a Gaussian function with FWHM = 1.8 kHz. d, e Hahn-echo decay. e, CPMG dynamical decoupling decay. The number of pairs of π-pulses is indicated in the inset. X and Y indicate the axes around which the spin is rotated, through the application of microwave pulses in-phase (X) or in-quadrature (Y) with the reference clock. The coherence times quoted in each panel are obtained by fitting the decays with functions of the form P0 exp(–(t/T2)n) + P. The decay exponent n is related to the frequency dependence of the power spectral density S(ω) of the noise that couples to the qubit (Supplementary Section E). The Hahn-echo and CPMG plots are normalized with respect to P0 and P. Data in c and e are from device B; all other data are from device A.

  3. Nuclear spin qubit.
    Figure 3: Nuclear spin qubit.

    ac, Nuclear spin coherence times obtained from Ramsey (a), Hahn-echo (b) and CPMG decay (c) measurements. Left column: neutral donor (31P0). Right column: ionized donor (31P+). For the CPMG sequences, the number of pairs of π-pulses is indicated in the insets. Fitting functions are of the form P(t) = P0 exp(−(t/T2)n) + P. All data are from device B. X and Y indicate the axes around which the spin is rotated, through the application of microwave pulses in-phase (X) or in-quadrature (Y) with the reference clock.

  4. Noise spectroscopy of the electron spin qubit.
    Figure 4: Noise spectroscopy of the electron spin qubit.

    a, Noise power spectral densities (S(ω)) for the electron spin qubit in device A (circles) and device B (squares). Solid lines are fits of the form C2/ω2.5 + C0, with the following parameters: C2 = 6 × 1011, C0 = 10 for device A; C2 = 9 × 1011, C0 = 6 for device B. Dashed lines show the C2/ω2.5 and C0 terms separately for device B. b, Electron coherence times from CPMG pulse sequences as a function of the number N of refocusing pulses. Dashed lines are theoretical predictions assuming the noise spectral density from the solid-line fits in a. The excellent agreement between the calculated lines and the data at low N proves that the S(ω)  ω−2.5 dependence continues well below 1 kHz. With S(ω)  ω−α, the coherence time is expected to scale as Nα/(α+1) (ref. 28), yielding N0.71 for α = 2.5, which is shown in the figure as a guide to the eye (dotted line). Error bars are 95% confidence intervals from the exponential fits used to extract the decay times.

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Author information

Affiliations

  1. Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, UNSW Australia, Sydney, New South Wales 2052, Australia

    • Juha T. Muhonen,
    • Juan P. Dehollain,
    • Arne Laucht,
    • Fay E. Hudson,
    • Rachpon Kalra,
    • Andrew S. Dzurak &
    • Andrea Morello
  2. School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, 223-8522, Japan

    • Takeharu Sekiguchi &
    • Kohei M. Itoh
  3. Centre for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Melbourne, Victoria 3010, Australia

    • David N. Jamieson &
    • Jeffrey C. McCallum

Contributions

J.T.M., J.P.D., A.S.D. and A.M. designed the experiments. J.T.M., J.P.D. and A.L. performed the measurements and analysed the results with A.M.'s supervision. D.N.J. and J.C.M. designed the P implantation experiments. F.E.H. fabricated the device with A.S.D.'s supervision and R.K.'s assistance. T.S. and K.M.I. prepared and supplied the 28Si epilayer wafer. J.T.M., J.P.D and A.M. wrote the manuscript, with input from all co-authors.

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The authors declare no competing financial interests.

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