# Operation of a silicon quantum processor unit cell above one kelvin

## Abstract

Quantum computers are expected to outperform conventional computers in several important applications, from molecular simulation to search algorithms, once they can be scaled up to large numbers—typically millions—of quantum bits (qubits)1,2,3. For most solid-state qubit technologies—for example, those using superconducting circuits or semiconductor spins—scaling poses a considerable challenge because every additional qubit increases the heat generated, whereas the cooling power of dilution refrigerators is severely limited at their operating temperature (less than 100 millikelvin)4,5,6. Here we demonstrate the operation of a scalable silicon quantum processor unit cell comprising two qubits confined to quantum dots at about 1.5 kelvin. We achieve this by isolating the quantum dots from the electron reservoir, and then initializing and reading the qubits solely via tunnelling of electrons between the two quantum dots7,8,9. We coherently control the qubits using electrically driven spin resonance10,11 in isotopically enriched silicon12 28Si, attaining single-qubit gate fidelities of 98.6 per cent and a coherence time of 2 microseconds during ‘hot’ operation, comparable to those of spin qubits in natural silicon at millikelvin temperatures13,14,15,16. Furthermore, we show that the unit cell can be operated at magnetic fields as low as 0.1 tesla, corresponding to a qubit control frequency of 3.5 gigahertz, where the qubit energy is well below the thermal energy. The unit cell constitutes the core building block of a full-scale silicon quantum computer and satisfies layout constraints required by error-correction architectures8,17. Our work indicates that a spin-based quantum computer could be operated at increased temperatures in a simple pumped 4He system (which provides cooling power orders of magnitude higher than that of dilution refrigerators), thus potentially enabling the integration of classical control electronics with the qubit array18,19.

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## Data availability

The datasets generated and/or analysed during this study are available from the corresponding authors on reasonable request.

## Code availability

The analysis codes that support the findings of the study are available from the corresponding authors on reasonable request.

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## Acknowledgements

We acknowledge support from the US Army Research Office (W911NF-17-1-0198), the Australian Research Council (CE170100012), Silicon Quantum Computing Proprietary Limited and the NSW Node of the Australian National Fabrication Facility. 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 Army Research Office or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. K.M.I. acknowledges support from a Grant-in-Aid for Scientific Research by MEXT. J.C.L. and M.P.-L. acknowledge support from the Canada First Research Excellence Fund and in part by the National Science Engineering Research Council of Canada. K.Y.T. acknowledges support from the Academy of Finland through projects 308161, 314302 and 316551. This work was funded in part by Silicon Quantum Computing Proprietary Limited.

## Author information

Authors

### Contributions

C.H.Y. designed and performed the experiments. C.H.Y., R.C.C.L. and A.S. analysed the data. J.C.C.H. and F.E.H. fabricated the device under A.S.D.’s supervision. J.C.C.H., T.T. and W.H. contributed to the preparation of the experiments. J.C.L., R.C.C.L., J.C.C.H., C.H.Y. and M.P.-L. designed the device. K.W.C. and K.Y.T. contributed to discussions on the nanofabrication process. K.M.I. prepared and supplied the 28Si epilayer. T.T., W.H., A.M. and A.L. contributed to the discussion and interpretation of the results. C.H.Y., A.S., A.L. and A.S.D. wrote the manuscript with input from all co-authors.

### Corresponding authors

Correspondence to C. H. Yang or A. S. Dzurak.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks John Gamble, HongWen Jiang 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 figures and tables

### Extended Data Fig. 1 Experimental setup.

The device measured is identical to the one described in ref. 11. It is fabricated on an isotopically enriched 900-nm-thick 28Si epilayer12 with 800 ppm residual concentration of 29Si using multi-layer gate-stack silicon MOS technology39,40. Rechargeable isolated voltage source modules (SIM928 from Stanford Research System, SRS, mounted in SRS SIM900 mainframes) are used to supply all our d.c. (DC) voltages, and a LeCroy ArbStudio 1104 arbitrary waveform generator (AWG) is combined with the d.c. voltages through resistive voltage dividers, with 1/5 division for the d.c. and 1/25 for the AWG inputs. The resistance of the voltage dividers in combination with the capacitance of the coaxial cables limits the AWG bandwidth to ~5 MHz. Filter boxes with lowpass filtering (100 Hz for d.c. lines and 80 MHz for fast lines) and thermalization are mounted on the mixing chamber (MC) plate. Shaped microwave (MW) pulses are delivered by an Agilent E8267D vector signal generator, employing its own internal AWG for in-phase/quadrature (IQ) modulation. There are two d.c. blocks and two attenuators along the microwave line, as indicated in the schematic. The SET sensor current signal is amplified by a FEMTO DLPCA-200 transimpedance amplifier and an SRS SIM910 JFET isolation amplifier with gain of 100, before passing an SRS SIM965 lowpass filter and finally being acquired by an Alazar ATS9440 digitizer. The SpinCore PBESR-PRO-500 pulse generator acts as the master trigger source for all other instruments. The device sits inside an Oxford Kelvinox 100 wet dilution refrigerator with base temperature TMC = 40 mK. The superconducting magnet is powered by an American Magnet Inc. AMI430 power supply. CH1–CH4, physical channel input/output 1–4 from the instruments.

### Extended Data Fig. 2 Qubit spectra in the (3, 3) charge configuration region.

EDSR spectra of Q1 (lower frequency) and Q2 (upper frequency) as a function of ΔVG = VG1 − VG2, measured using adiabatic microwave pulses with frequency sweep range ΔfAdb = 2 MHz and pulse time τAdb = 0.5 ms, at B0 = 1.4 T and TMC = 40 mK. The cobalt magnet is designed to minimize the magnetic field difference between the two QDs. The bending of the spectrum of Q2 suggests strong mixing with an excited state. Near the (4, 2) region, both spectra split up equally owing to the increase of J coupling. A small splitting can also been seen near the (2, 4) region. At the (2, 4) and (4, 2) electron charge transitions, we no longer have a proper effective two-spin system and the signal vanishes. We operate our qubits mostly near the (2, 4) side (left) for faster EDSR control over Q1.

### Extended Data Fig. 3 Qubit spectra in other charge configurations.

a, b, EDSR spectra of the (3, 3) (a) and (1, 3) (b) charge configurations as a function of ΔVG = VG1 − VG2 at B0 = 0.5 T and TMC = 40 mK. Between (3, 3) and (1, 3), the number of electrons in Q1 changes, but it remains constant in Q2. Whereas the bending spectrum exhibits minimal change in frequency and can be attributed to Q2, the straight spectrum shifts by more than 50 MHz, confirming that it corresponds to Q1. The large change in the frequency of Q1 is mainly due to the unpaired-electron spin now occupying the other valley state. c, For large VJ, a third QD starts forming under the J gate (compare with Fig. 1), and the device can be operated as a two-qubit system with two electrons in the (1, 0, 1) and (0, 1, 1) configurations at B0 = 1.4 T and TMC = 40 mK. Only one qubit resonance is clearly found, whereas the other one is only weakly observed when J coupling increases (red circle), where spin–orbit coupling is stronger for the tightly confined dot. Inset, J coupling increases with VJ, demonstrating control of J when moving one electron from the (1, 0, 1) to the (0, 1, 1) charge configuration.

### Extended Data Fig. 4 Spin relaxation measurements using parity readout.

ac, PZZ with | initialization and flipping the spin of Q1 adiabatically via EDSR (|) (a), no spin flip (|) (b) and flipping the spin of Q2 adiabatically (|) (c). df, PZZ with S-like initialization and flipping the spin of Q1 adiabatically (d), no spin flip (e) and flipping the spin of Q2 adiabatically via EDSR (f). The measurements were performed at B0 = 1.4 T and TMC = 40 mK. Each data point is the average of 100 single shots, with three overall repeats, giving a total of 300 single shots. All fits are according to equations (9)–(14). The error range of T1 represents the 95% confidence level.

### Extended Data Fig. 5 CNOT operation via exchange gate pulsing.

Data measured at B0 = 0.8 T and TMC = 40 mK. a, EDSR spectra of Q1 and Q2 as a function of voltage ΔVJ applied to gate J. At large ΔVJ, the resonance lines clearly split, demonstrating control over the J coupling. b, Pulse sequence of a CNOT-like two-qubit gate. c, d, Measured and simulated parity readout (PZZ) after applying the pulse sequence in b, as a function of ΔfQ2 and exchange pulse time τJ, for VCZ = 30 mV. Here, VG1 is also pulsed at 20% of VCZ to maintain a constant charge detuning. The CZ fidelity is >90%, as confirmed by observing no substantial decay over four CZ cycles. The simulated Hamiltonian uses a σZI coefficient of 370 kHz and a σZZ coefficient of 89 kHz. The good agreement with the experimental data validates the performance of the CNOT gate. e, f, As in c, d, but with VCZ = 32 mV. The simulated Hamiltonian has a σZI coefficient of 290 kHz and a σZZ coefficient of 135 kHz. Small charge rearrangement occurs in the device between c and e.

### Extended Data Fig. 6 Effective electron temperature of the isolated QD unit cell.

a, Charge occupation probability around the (2, 4)–(3, 3) charge transition, measured through ISET using a triangular wave with a peak-to-peak voltage of ΔVGp–p = 8 mV applied to ΔVG. δΔVG is the rebiased ΔVG value for which the fitted charge transitions occur at 0 V. The solid lines are fits to the Fermi distribution, which we use to extract the effective electron temperature as a function of mixing chamber temperature. b, Effective electron temperatures extracted from a. The effective temperature is calculated using the lever arm from Extended Data Fig. 7. The minimum effective electron temperature is ~250 mK at low mixing chamber temperatures. At higher temperatures, the effective electron temperature is equal to the mixing chamber temperature. Measured at B0 = 0 T. Error bars represent the 95% confidence level.

### Extended Data Fig. 7 Magnetospectroscopy of the (2, 4) and (3, 3) charge configurations.

The transitions that move with the magnetic field are caused by Zeeman splitting, allowing us to extract the lever arm of VG1 as 0.2128. Because ΔVGp−p = ΔVG1 − ΔVG2, and the pulse is applied symmetrically to both G1 and G2, we can further extract the lever arm of VG2 to be $$0.2128\times \frac{36.8\,{\rm{mV}}-20\,{\rm{mV}}}{40\,{\rm{mV}}-20\,{\rm{mV}}}=0.1788$$. The valley splitting energy of the QDs can be approximated as 600 μeV, where the blockaded region at (3, 3) corresponds to the splitting energy. Further evidence can be found in ref. 11, where no valley splitting below 600 μeV was observed in the low-electron-number regime for this same QD device. g, g-factor of electron in silicon (g = 2); μB, Bohr magneton; e, electron charge; ΔEV1, valley splitting energy of QD1.

### Extended Data Fig. 8 Magnetic field dependence of qubit properties.

ac, Spin relaxation time T1 (a), Hahn Echo coherence time $${T}_{2}^{{\rm{Hahn}}}$$ (b) and Ramsey coherence time $${T}_{2}^{* }$$ (c) as a function of external magnetic field B0. Error bars represent the 95% confidence level.

### Extended Data Fig. 9 Readout visibility of the SET charge sensor.

ad, Histograms of the charge sensor current $$\Delta {I}_{{\rm{SET}}}={\bar{I}}_{{\rm{SET}}}({\rm{read}})-{\bar{I}}_{{\rm{SET}}}({\rm{reset}})$$ for Fig. 3a (a; TMC = 40 mK, B0 = 0.1 T), Fig. 3b (b; TMC = 40 mK, B0 = 1.4 T), Fig. 3e (c; TMC = 1.5 K, B0 = 0.1 T) and Fig. 3f (d; TMC = 1.5 K, B0 = 1.4 T). The histograms in a, b are fitted with a Gaussian model including decay from the even-parity state to the odd-parity state during the readout period41. The extracted visibilities are 88.1% (a) and 89.3% (b). Assuming no state decay during readout, the ideal readout visibility, which corresponds to the charge readout visibility, would be Videal = 99.9% for TMC = 40 mK. The histograms in c, d are fitted to the ideal Gaussian model only, giving Videal = 78.5% and Videal = 79.5% for TMC = 1.5 K. This clearly highlights the limitations of SET charge sensing at increased temperatures, owing to the thermal distribution of electrons in the SET source and drain reservoirs. The insets show example ISET traces for odd- and even-parity state readout, with the horizontal axis showing the time from 0.2 μs to 4.5 μs, the vertical axis showing the current up to 200 pA (arbitrarily shifted), and a measurement bandwidth of 3 kHz .

### Extended Data Fig. 10 Expanded randomized benchmarking data.

a, Complete datasets of the randomized benchmarking data in Fig. 3d (TMC = 40 mK, B0 = 1.4 T), with a total of 102 repetitions of a randomized sequence, with Clifford gate lengths {1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, 25, 32, 40, 50, 63, 79, 100, 126, 158, 200, 251, 316, 398, 501, 631, 794, 1,000}. b, Complete datasets of the randomized benchmarking data in Fig. 3h (TMC = 1.5 K, B0 = 1.4 T), with a total of 280 repetitions of a randomized sequence, with Clifford gate lengths {1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, 25, 32, 40, 50, 63, 79, 100}.

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Yang, C.H., Leon, R.C.C., Hwang, J.C.C. et al. Operation of a silicon quantum processor unit cell above one kelvin. Nature 580, 350–354 (2020). https://doi.org/10.1038/s41586-020-2171-6

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