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 solidstate 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 dots^{7,8,9}. We coherently control the qubits using electrically driven spin resonance^{10,11} in isotopically enriched silicon^{12} ^{28}Si, attaining singlequbit 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 temperatures^{13,14,15,16}. 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 fullscale silicon quantum computer and satisfies layout constraints required by errorcorrection architectures^{8,17}. Our work indicates that a spinbased quantum computer could be operated at increased temperatures in a simple pumped ^{4}He 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 array^{18,19}.
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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 (W911NF1710198), 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 GrantinAid 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.
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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 ^{28}Si 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 coauthors.
Corresponding authors
Correspondence to C. H. Yang or A. S. Dzurak.
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The authors declare no competing interests.
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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.
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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 900nmthick ^{28}Si epilayer^{12} with 800 ppm residual concentration of ^{29}Si using multilayer gatestack silicon MOS technology^{39,40}. 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 inphase/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 DLPCA200 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 PBESRPRO500 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 T_{MC} = 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 Q_{1} (lower frequency) and Q_{2} (upper frequency) as a function of ΔV_{G} = V_{G1} − V_{G2}, measured using adiabatic microwave pulses with frequency sweep range Δf_{Adb} = 2 MHz and pulse time τ_{Adb} = 0.5 ms, at B_{0} = 1.4 T and T_{MC} = 40 mK. The cobalt magnet is designed to minimize the magnetic field difference between the two QDs. The bending of the spectrum of Q_{2} 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 twospin system and the signal vanishes. We operate our qubits mostly near the (2, 4) side (left) for faster EDSR control over Q_{1}.
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 ΔV_{G} = V_{G1} − V_{G2} at B_{0} = 0.5 T and T_{MC} = 40 mK. Between (3, 3) and (1, 3), the number of electrons in Q_{1} changes, but it remains constant in Q_{2}. Whereas the bending spectrum exhibits minimal change in frequency and can be attributed to Q_{2}, the straight spectrum shifts by more than 50 MHz, confirming that it corresponds to Q_{1}. The large change in the frequency of Q_{1} is mainly due to the unpairedelectron spin now occupying the other valley state. c, For large V_{J}, a third QD starts forming under the J gate (compare with Fig. 1), and the device can be operated as a twoqubit system with two electrons in the (1, 0, 1) and (0, 1, 1) configurations at B_{0} = 1.4 T and T_{MC} = 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 V_{J}, 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.
a–c, P_{ZZ} with ⇊⟩ initialization and flipping the spin of Q_{1} adiabatically via EDSR (⇅⟩) (a), no spin flip (⇊⟩) (b) and flipping the spin of Q_{2} adiabatically (⇵⟩) (c). d–f, P_{ZZ} with Slike initialization and flipping the spin of Q_{1} adiabatically (d), no spin flip (e) and flipping the spin of Q_{2} adiabatically via EDSR (f). The measurements were performed at B_{0} = 1.4 T and T_{MC} = 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 T_{1} represents the 95% confidence level.
Extended Data Fig. 5 CNOT operation via exchange gate pulsing.
Data measured at B_{0} = 0.8 T and T_{MC} = 40 mK. a, EDSR spectra of Q_{1} and Q_{2} as a function of voltage ΔV_{J} applied to gate J. At large ΔV_{J}, the resonance lines clearly split, demonstrating control over the J coupling. b, Pulse sequence of a CNOTlike twoqubit gate. c, d, Measured and simulated parity readout (P_{ZZ}) after applying the pulse sequence in b, as a function of Δf_{Q2} and exchange pulse time τ_{J}, for V_{CZ} = 30 mV. Here, V_{G1} is also pulsed at 20% of V_{CZ} 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 σ_{ZI} coefficient of 370 kHz and a σ_{ZZ} 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 V_{CZ} = 32 mV. The simulated Hamiltonian has a σ_{ZI} coefficient of 290 kHz and a σ_{ZZ} 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 I_{SET} using a triangular wave with a peaktopeak voltage of ΔV_{Gp–p} = 8 mV applied to ΔV_{G}. δΔV_{G} is the rebiased ΔV_{G} 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 B_{0} = 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 V_{G1} as 0.2128. Because ΔV_{Gp−p} = ΔV_{G1} − ΔV_{G2}, and the pulse is applied symmetrically to both G_{1} and G_{2}, we can further extract the lever arm of V_{G2} 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 lowelectronnumber regime for this same QD device. g, gfactor of electron in silicon (g = 2); μ_{B}, Bohr magneton; e, electron charge; ΔE_{V1}, valley splitting energy of QD_{1}.
Extended Data Fig. 8 Magnetic field dependence of qubit properties.
a–c, Spin relaxation time T_{1} (a), Hahn Echo coherence time \({T}_{2}^{{\rm{Hahn}}}\) (b) and Ramsey coherence time \({T}_{2}^{* }\) (c) as a function of external magnetic field B_{0}. Error bars represent the 95% confidence level.
Extended Data Fig. 9 Readout visibility of the SET charge sensor.
a–d, 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; T_{MC} = 40 mK, B_{0} = 0.1 T), Fig. 3b (b; T_{MC} = 40 mK, B_{0} = 1.4 T), Fig. 3e (c; T_{MC} = 1.5 K, B_{0} = 0.1 T) and Fig. 3f (d; T_{MC} = 1.5 K, B_{0} = 1.4 T). The histograms in a, b are fitted with a Gaussian model including decay from the evenparity state to the oddparity state during the readout period^{41}. 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 V_{ideal} = 99.9% for T_{MC} = 40 mK. The histograms in c, d are fitted to the ideal Gaussian model only, giving V_{ideal} = 78.5% and V_{ideal} = 79.5% for T_{MC} = 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 I_{SET} traces for odd and evenparity 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 (T_{MC} = 40 mK, B_{0} = 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 (T_{MC} = 1.5 K, B_{0} = 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/s4158602021716
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