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A low-noise on-chip coherent microwave source

Nature Electronics volume 4, pages 885–892 (2021)Cite this article

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Abstract

The scaling up of quantum computers operating in the microwave domain requires advanced control electronics, and the use of integrated components that operate at the temperature of the quantum devices is potentially beneficial. However, such an approach requires ultralow power dissipation and high signal quality to ensure quantum-coherent operations. Here we report an on-chip device that is based on a Josephson junction coupled to a spiral resonator and is capable of coherent continuous-wave microwave emission. We show that the characteristics of the device accurately follow a theory based on the perturbative treatment of a capacitively shunted Josephson junction as the gain element. The infidelity of typical quantum gate operations due to phase noise of this cryogenic 25 pW microwave source is less than 0.1% up to 10 ms evolution time, which is below the infidelity caused by dephasing in state-of-the-art superconducting qubits. Together with future cryogenic amplitude and phase modulation techniques, our approach may lead to scalable cryogenic control systems for quantum processors.

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Fig. 1: Working principle and device structure.
Fig. 2: Characteristics of the spiral-resonator source.
Fig. 3: Emission spectrum with injection locking.
Fig. 4: Noise properties of the on-chip source with injection locking.

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Data availability

Data supporting the findings of this study are available at https://zenodo.org/record/5571377#.YWlENrhByUk.

Code availability

The algorithms used for the findings of this study are available within the paper and files in the Supplementary Information.

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Acknowledgements

We have received funding from the Centre for Quantum Engineering at Aalto under grant no. JVSG; European Research Council under grant no. 681311 (QUESS) and Marie Skłodowska-Curie grant no. 795159; and Academy of Finland through its Centres of Excellence Programme (project nos. 336810, 312300, 312059 and 312295 and grant nos. 314447, 314449, 316551 and 335460). We thank H. Sipola, R. Kokkoniemi, J.-P. Girard, O.-P. Saira and J. Pekola for useful discussion.

Author information

Authors and Affiliations

  1. QCD Labs, QTF Centre of Excellence and Department of Applied Physics, Aalto University, Aalto, Finland

    Chengyu Yan, Jinli Zhang, Joni Ikonen, Jan Goetz & Mikko Möttönen

  2. MOE Key Laboratory of Fundamental Physical Quantities Measurement & Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan, People’s Republic of China

    Chengyu Yan

  3. IQM, Espoo, Finland

    Juha Hassel & Jan Goetz

  4. QTF Centre of Excellence, VTT Technical Research Centre of Finland Ltd., Espoo, Finland

    Juha Hassel, Visa Vesterinen, Leif Grönberg & Mikko Möttönen

  5. College of Electronic Information and Optical Engineering, Nankai University, Tianjin, People’s Republic of China

    Jinli Zhang

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Contributions

C.Y. conducted the experiments and data analysis with inputs from the other authors. J.H. developed the analytical model and contributed to the data analysis. J.H. and V.V. designed the device with input from L.G. who fabricated the sample. J.Z. and J.I. assisted in the heterodyne detection. C.Y., J.H., J.G. and M.M. conceived the experimental idea. The manuscript was written by C.Y., J.H. and M.M. with comments from all the authors. M.M. acted as the main supervisor of the work.

Corresponding authors

Correspondence to Chengyu Yan or Mikko Möttönen.

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Competing interests

The authors declare the following: M.M. is a co-founder and Chief Scientist of IQM. Some of the authors are inventors in the granted patent titled ‘Vector signal generator operating on microwave frequencies, and method for generating time-controlled vector signals on microwave frequencies (FI128904B)’ applied by Aalto University Foundation Sr. and VTT Technical Research Centre of Finland and invented by M.M., J.H., T. Ollikainen, and J.G. Patent nos. CN111697926A, WO2020183060A1 and TW202107837A belonging to the same patent family have been applied by IQM. These patents relate to the work reported in this manuscript in a way that the invention involves, but is not limited to, a voltage-biased Josephson junction for microwave generation.

Additional information

Peer review information Nature Electronics thanks Johannes Fink, Gary Steele and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Details of the spiral-resonator sample.

Schematic layered structure of the device in the vicinity of the Josephson junction. The AlOx layer deposited after the second niobium layer is not shown for clarity, but instead, the positions of the contact holes for the galvanic connections between the second and the third niobium layer are highlighted by the red rectangles. The Josephson junction is formed at the topmost region where the first and second niobium layers cross by selective etching and side-wall passivation of the first layer before the deposition of the second layer. This schematic figure corresponds to the area enclosed by the red rectangle in Fig. 1d.

Extended Data Fig. 2 Schematic experimental setup.

The output of the source is channeled either to the heterodyne setup (left position of the switch) or to the spectrum analyzer (right position of the switch). The millikelvin bias tee is used to combine the direct bias current with the possible injection tone. When the switch is at the left position, we do not use the isolators in between the source and the first amplifier, but a 3-dB attenuator instead. Some components of minor importance are not shown for the sake of clarity.

Extended Data Fig. 3 Stability diagram of a Josephson oscillator and trade-off between stability and power efficiency.

a, Total microwave load R1 for the oscillator to exhibit stable sustained oscillation as a function of the direct current through the junction 〈IJ〉. The load values are given relative to the optimum load corresponding to \({R}_{1}\approx 0.68\frac{\pi {I}_{{{{\rm{c}}}}}}{{\Phi }_{0}{C}_{{{{\rm{S}}}}}^{2}{\omega }^{3}}\) noting that 1/Qt ∝ R1. The bias point 〈IJ〉/Ic ≈ 0.58 provides the maximum power for the optimal load but is unstable against any variations of the load. For lower bias points, the range of allowed relative loads is finite and lies between the shown minimum and maximum. b, Computed total efficiency of the microwave generation ηtot as a function of 〈IJ〉 with the assumption of unconditional stability and single-valued bias path (see Supplementary Section 2). In this case, the total efficiency is a product of the direct-current (d.c.) efficiency ηdc and the microwave efficiency ηmw. If the output load of the device can be considered fixed, we may lift the requirement of unconditional stability and the microwave efficiency can be engineered to unity at relevant values of 〈IJ〉. If the Shapiro step can be found by other means than the single-valued bias path, the d.c. efficiency can be taken to unity.

Extended Data Fig. 4 Measured probability distribution of the spiral-resonator source without injection locking.

a, Probability distribution of the output signal in the in-phase–quadrature (IQ) plane after digital down-conversion and filtering (see Supplementary Section 3) of the data for Fig. 2d. b, Probability distribution of the normalized photon number for the data in a. The blue colour shows the experimental data and the solid red line is a corresponding Gaussian fitting with a full width at half maximum of 0.037. c, Extracted phase from the IQ measurement of a real-time trace after down-conversion and filtering. Occasionally, we observe enhanced noise which we attribute to the heterodyne measurement setup. Thus, these data are not used for the evaluation of the phase noise of the source.

Extended Data Fig. 5 Emission spectrum of the spiral-resonator source under injection locking.

a-d, Measured power spectral density with respect to the output of the source as a function of the spectral frequency fSA and of the injection frequency finj at a fixed injection power as indicated. In a, we provide a three-dimensional image to highlight the sharpness of the peaks. The dashed lines provide the predictions of the peak positions from the Adler theory. In b, Δf is defined as the width of the frequency range where the emission signal is phase locked to the injection tone.

Extended Data Fig. 6 Illustration of the sample and measurement results for the microwave source based on a lumped-element resonator.

a, False-colour scanning-electron-microscope image of a lumped-element device nominally identical to that measured. The ground plane is denoted by red colour. The bias line and the lumped-element resonator, consisting of a straight inductive strip L1, and an AlOx parallel-plate capacitor C1, is highlighted in yellow. The shunt capacitor Cs appears in cyan colour. The coupling capacitance C2 is shown in magenta. The scratches and black dots on the surface are not present on the measured device. The layered structure of the Josephson junction is identical to that in the spiral-resonator device, apart from the junction area of roughly 3 μm2. The scale bar is 60 μm. b, Power spectral density emitted from the source as a function of the bias current and emission frequency. The red dashed trace indicates the position of the emission peak predicted by equation (S1). c, Voltage measured across the junction as a function of bias current. d, Output power as a function of bias current. The measured data (red dots) are in good agreement with equation (S11) (blue solid trace). e, Measured probability distribution of the source output in the in-phase–quadrature (IQ) plane at Ib = 3.2 μA obtained using the heterodyne measurement setup.

Extended Data Fig. 7 Effect of the subtraction of the noise floor on the phase noise and calculated operation fidelity of the injection-locked spiral-resonator source.

a, Measured phase noise of the source before (red) and after (black) the subtraction of the noise floor. The noise floor is measured after turning off the local oscillator and the bias current of the source. To obtain the phase noise with the noise floor subtracted, a careful averaging is carried out within the frequency range indicated by the two-headed arrow. We average both the original signal and the noise floor in order to mitigate the fluctuations in the phase noise. b, Calculated bound for the operation infidelity corresponding to the data in a before (solid lines) and after (dashed lines) the subtraction of the noise floor for Ramsey (blue colour), Hahn echo (red colour), and NOT gate (green colour) operations.

Extended Data Fig. 8 Detailed analysis of the linewidth of the output signal under 100-dBm injection locking.

Measured (markers) power spectral density of the spiral-resonator output signal as a function of frequency offset from the injection tone. Note the logarithmic scale on the vertical axis as opposed to the linear scale in Fig. 3b for these data. The resolution of the spectrum analyzer is set to 1 Hz, leading to a least-square Gaussian fit with a full width at half maximum (FWHM) of 0.97 Hz (red line). We also show Voigt fits corresponding to 1-Hz FWHM of the Gaussian component and FWHM of 1 mHz (magenta line) and 10 mHz (yellow line) for the Lorentzian components. The four data points at the lowest and highest frequency offsets (grey colour) are significantly affected by the non-ideality of the Gaussian filter in the used spectrum analyzer, and consequently cannot be interpreted to reflect the line broadening of the source itself. See Supplementary Section 6 for the discussion.

Extended Data Fig. 9 Output power requirement in qubit gate drive.

The number of qubits drivable with an oscillator power of 25 pW, as a function of the Purcell decay rate for different indicated gate lengths. See Supplementary Section 7 for the discussion.

Supplementary information

Supplementary Information

Supplementary Figs. 1–4 and Sections 1–7.

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Yan, C., Hassel, J., Vesterinen, V. et al. A low-noise on-chip coherent microwave source. Nat Electron 4, 885–892 (2021). https://doi.org/10.1038/s41928-021-00680-z

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