Abstract
The silicon metaloxidesemiconductor (MOS) material system is a technologically important implementation of spinbased quantum information processing. However, the MOS interface is imperfect leading to concerns about 1/f trap noise and variability in the electron gfactor due to spin–orbit (SO) effects. Here we advantageously use interface–SO coupling for a critical control axis in a doublequantumdot singlet–triplet qubit. The magnetic fieldorientation dependence of the gfactors is consistent with Rashba and Dresselhaus interface–SO contributions. The resulting allelectrical, twoaxis control is also used to probe the MOS interface noise. The measured inhomogeneous dephasing time, \(T_{{\mathrm{2m}}}^ \star\), of 1.6 μs is consistent with 99.95% ^{28}Si enrichment. Furthermore, when tuned to be sensitive to exchange fluctuations, a quasistatic charge noise detuning variance of 2 μeV is observed, competitive with lownoise reports in other semiconductor qubits. This work, therefore, demonstrates that the MOS interface inherently provides properties for twoaxis qubit control, while not increasing noise relative to other material choices.
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Introduction
Spin qubits in silicon metaloxidesemiconductor (MOS) structures offer a promising path towards implementing quantum information processing. The MOS system combined with enriched ^{28}Si provides a magnetic vacuum^{1} and promises to leverage the extensive complementary metaloxidesemiconductor (CMOS) fabrication platform. Recently, several critical demonstrations have shown long spin coherence times^{2}, twoqubit couplings of single spins in a multiquantum dot layout^{3}, large tunable valleysplitting^{2,4,5}, and importantly similar valley splittings in different process flows and multiple devices^{4,5}. Yet, there are persistent concerns about the intrinsically imperfect Si/SiO_{2} interface produces persistent concerns about charge noise from the disordered interface. Two potentially key performance challenges identified are extra detrimental charge noise and variable gfactors^{6,7}.
Charge traps and twolevel fluctuators near the interface are believed to be potential sources of noise in MOS devices^{8,9,10}. To attempt to suppress the challenges of disorder and trap noise Si quantum dot (QD) spin qubits have also been developed in heteroepitaxial Si/SiGe^{11,12,13,14,15,16}. The imperfect crystal–dielectric interface is shifted further away. This is the predominant choice despite reports of difficulties with small or variable valleysplitting^{13,14,15,17}. Nevertheless qubits have successfully been demonstrated and charge noise has been studied in Si/SiGe qubits^{12,16,18,19}, but only indirect measures of charge noise in MOS qubits have been reported^{3,20,21}. Direct characterization of charge noise at the MOS interface is needed for comparison.
Variability in gfactors recently observed in silicon QDs is also feared to introduce potentially challenging complications for many qubit device architectures^{7}. In bulk Si, the spin–orbit (SO) interaction leads to only weakly perturbed electron gfactors that are close to g = 2. However, the inversion asymmetry of the crystal at an interface leads to a SO interaction^{22,23,24,25}, as shown in Fig. 1. When a magnetic field is applied with a component parallel to the interface, electron cyclotron motion establishes a nonzero net momentum component along the interface (Fig. 1a). The coupling of the electron momentum perpendicular to the effective electric field at the interface produces the SO interaction. The vertical electric potential at the interface leads to a Rashba SO contribution due to structural inversion asymmetry (SIA). A second interaction, the Dresselhaus contribution, is attributed to microscopic interface inversion asymmetry (IIA)^{26}, due to the largely unknown and possibly position dependent interatomic electric fields at the Si/SiO_{2} boundary. Recent work has attributed the variability in electron gfactor at silicon interfaces to SO coupling and interface disorder^{2,6,27,28,29,30}. However, while the effects of vertical electric field and inplane magnetic field direction have been observed, the full dependence on magnetic field strength and orientation has not, to date, been characterized in the MOS material system. We further note that this interface effect is not theoretically unique to Si MOS or SiGe/Si interfaces^{22,23,31} and variability in gfactor has also been observed in GaAs/AlGaAs QDs^{32,33}, as well as holes in silicon QDs^{34}. Because of its strength and angular dependence, which is similar to bulk SO effects, it is possible that the contribution of the interface effect, particularly on the Dresselhaus coupling, is underappreciated in other systems that leverage strong SO coupling. Improved understanding of this effect has the potential to influence areas such as spintronics and the pursuit of forming topological states of matter^{35,36}.
In this work, we advantageously use the inherent gfactor difference from the SO coupling at the Si/SiO_{2} interface to create a second axis of control for a doublequantum dot (DQD) singlet–triplet (ST) qubit. This first demonstration of an allelectrical, twoaxis controlled qubit in MOS is used to study qubit noise and SO interaction at the dielectric interface. One of the central results of this paper is a quantitative characterization of charge noise in a MOS qubit (e.g., quasistatic detuning variance and Hahnecho time). The magnitudes are comparable if not better than those reported for other semiconductor qubit materials like GaAs/AlGaAs and Si/SiGe. The second central result of this paper is that we demonstrate a SO ST qubit and use its coherent qubit rotations to characterize the SO interaction at the MOS interface over its full magnetic field angular dependence. We observe that, by choice of external magnetic field orientation, the intrinsic SO interaction may be maximized to drive spin rotations or canceled out, which may be important for applications where uniform spin splitting between many QDs is necessary. In particular, an outofplane magnetic field orientation, measured in this work, should uniformly suppress the SO effect. We additionally extend the theoretical framework for the interface Rashba–Dresselhaus coupling providing a gauge independent phenomenological effective mass description of the full angular dependence that is in quantitative agreement with experiment. This work, therefore, further advances our understanding of the silicon MOS interface as a potential stateoftheart platform for quantum information technologies.
Results
SO ST qubit
The qubit in this work is formed within a MOS doublequantum dot (DQD). Two electrons are electrostatically confined within a double well potential, where the dominant interaction between the electrons can be electrically tuned between two regimes for twoaxis control (Fig. 1c). When the electronic wave functions of the QDs overlap significantly, the exchange energy, J, dominates. When the two electrons are well separated, J is small and distinct Zeeman energies result from the differences in their interface–SO coupling. The difference in SO coupling leads to a variation in effective electron gfactors (Fig. 1e) This amounts to an effective magnetic field gradient between the QDs that can be tuned with control of the applied electric and magnetic fields. Thus, we achieve allelectrical twoaxis control using native features of the MOS DQD system, avoiding the substantial fabrication complications to add a second axis of control for other Si qubit schemes.
We define the computational basis as the eigenstates of the twospin system in the limit of a large singlet–triplet exchange energy, J. Specifically, these are the two states, S and T_{0}, of the m = 0 subspace, which form a decoherencefree subspace relative to fluctuations in a uniform magnetic field^{37}. An applied magnetic field splits the m = ±1 spin triplet states (T_{±} (1, 1)) and m = 0 states by the Zeeman energy E_{Z} = gμ_{B}B to isolate the m = 0 subspace. A qubit state can then be initialized in a singlet ground state when the two QDs are electrically detuned out of resonance such that it is preferable to have a \(( {N_{{\mathrm{QD}}_{\mathrm{1}}},N_{{\mathrm{QD}}_{\mathrm{2}}}} )\) = (2, 0) charge state (Fig. 1c). Rapid adiabatic passage to the (1, 1) charge state produces a superposition of the S and T_{0} eigenstates in the gradient field. A difference in the Larmor spin precession frequency of the two QDs induces Xrotations between the S(1, 1) and T_{0}(1, 1) states (Figs. 1f and 2a). For each QD the angular precession frequency is given by ω = gμ_{B}B/ħ, where g is the electron gfactor, μ_{B} is the Bohr magneton, ħ is Planck’s constant, and B is the applied magnetic field. The twoelectron spin qubit will oscillate between the S and T_{0} states at a frequency 2πf = Δω = Δgμ_{B}B/ħ, where Δg is the difference in electron gfactor between the two QDs. Zrotations can be turned on by shifting the detuning closer to the charge anticrossing where J is larger, driving oscillations around the equator of the Bloch sphere (Fig. 1c). The spin state is detected using Pauli blockade, combined with a remote charge sensor that detects whether the qubit state passed through the (2, 0) charge state or was blockaded in (1, 1) during the readout stage^{38}.
SOdriven spin rotations
The spin splitting of an electron in a QD is governed by an effective Zeeman Hamiltonian of the form \(H_{{\mathrm{eff}}} = \frac{{\mu _{\rm B}}}{2}{\bf{B}} \cdot {\bf{g}} \cdot {\bf{\sigma }}\), where B is the magnetic field vector, σ is the vector of Pauli spin matrices (σ_{ x }, σ_{ y }, σ_{ z }) and g is the electron gtensor. An electron confined to an interface will have Rashba and Dresselhaus SO couplings of the form H_{R} ∝ γ_{R}(P_{ y }σ_{ x } − P_{ x }σ_{ y }) and H_{D} ∝ γ_{D}(P_{ x }σ_{ x } − P_{ y }σ_{ y }), respectively, where γ_{R} and γ_{D} are the relative coupling strengths. The operators σ_{ x }, σ_{ y } are Pauli spin matrices, while P_{ x }, P_{ y } are components of the kinetic momentum P = −iħ∇ + eA(r) along the [100], [010] direction, with e > 0 the elementary unit of charge and A(r) the vector potential. Including the H_{R} and H_{D} SO Hamiltonians perturbatively leads to an effective gtensor of the form
where g_{⊥} (g_{}) is the gtensor component for the directions perpendicular (parallel) to the [001] valley of bulk silicon. Corrections to the gtensor due to Rashba and Dresselhaus SO coupling are characterized by α and β, respectively. The strength of the SO interaction is predicted to depend on applied electric field, lateral confinement, valleyorbit configuration, and the atomicscale structure of the interface (see Supplementary Note 1 and refs. ^{6,27,28,30}). Consequently, the local interfacial and electrostatic environments particular to each QD produce differences in effective gtensor (Fig. 2f). This will act as a difference in effective inplane magnetic field, modifying the electron spin splitting between dots and drive rotations at a frequency
where ϕ is the field direction inplane of the interface with respect to the [100] crystallographic direction, θ is the outofplane angle relative to [001], and Δα and Δβ quantify the difference in Rashba and Dresselhaus gtensor perturbations between the two QDs, respectively. Our theoretical model for the SO coupling associated with the interface is discussed in greater detail in Supplementary Note 1 and is informed by the previous work of refs. ^{6,24,25,26,27,28}.
In Fig. 2b, we show the singlet return signal as a function of time spent at the manipulation point in (1,1) as the external magnetic field is varied along the \([1\bar 10]\) crystallographic direction. The observed oscillations demonstrate the ability to control coherent rotations. The rotation frequency displays a clear magnetic field dependence. In Fig. 2c, we plot the SOinduced rotation frequency as a function of field for both the [110] and \([1\bar 10]_{}^{}\) directions. The linear dependence on field is consistent with a gfactor difference between the two QDs (f = (Δg)μ_{B}B/h), whereas the difference in the slopes indicates an angular dependence for Δg. We plot the full angular dependence of the SO interaction in Fig. 2d and e. Figure 2d shows the measured difference in gyromagnetic ratio between the dots, (Δg)μ_{B}/h, as a function of the inplane angle ϕ relative to the [100] crystallographic direction. Dependence on the outofplane angle, θ, is shown in Fig. 2e. Here, ϕ is fixed along the [110] ([1\(\bar 1\)0]) direction and the measured difference in gyromagnetic ratio between the dots is plotted in blue (red) as the field is tilted out of the interface plane (θ = 0 is along the [001] direction). Qualitatively, the angular dependence is consistent with a SO effect, slightly different in each QD, composed of Rashba and Dresselhaus contributions. Enhanced interface–SO effects in Si have been surmised previously for inplane magnetic field dependences^{27,28,39,40,41}. We plot fits to Eq. (2) along with the data in Fig. 2d and e. We extract relative SO parameters Δα = 1.89 MHz T^{−1} and Δβ = 15.7 MHz T^{−1}. The maximum useful magnetic field is limited by state preparation and measurement (SPAM) errors as the S − T_{−} splitting becomes comparable to k_{B}T. The maximum rotation frequency achieved for the present electrostatic confinement was near 20 MHz for fields above 1 T along the \([1\bar 10]\) direction.
The ability to realize meaningful quantum information processing in MOS depends on the timescale over which environmental noise near the interface interacts with the qubit, Fig. 3c and d. Although sparse, the background ^{29}Si nuclear spins are sufficient in number to produce a slowly varying effective magnetic field, an Overhauser field. Nuclear spin flipflops lead to a timevariation of the Overhauser field that is quasistatic on the timescale of a single measurement instance, but can shift the rotation frequency in the time interval between measurements. A consequence of this effect is that the decay in time of the coherent oscillations depends on the measurement integration time, as has been observed previously in ST qubits^{12,42}. The longer an average measurement is done, the broader the distribution of spin configurations (i.e., Overhauser fields) sampled. The ensembleaveraged singlet return signal as a function of time spent driving rotations in the (1, 1) region, with an external magnetic field oriented along the \([1\bar 10]\) crystallographic axis, is shown in Fig. 3a. The decay in oscillation amplitude fits a Gaussian form consistent with quasistatic noise^{42}, and characteristic inhomogeneous dephasing time, \(T_{\mathrm{2}}^ \star\), is extracted assuming a functional time dependence of \({\mathrm{exp}}[ {  \left( {t{\mathrm{/}}T_{\mathrm{2}}^ \star } \right)^2} ]\) for the oscillation decay envelope.
In Fig. 3b, we examine the dependence of our results on measurement time and magnetic field. We find a longaveraging inhomogeneous dephasing time of \(T_{\mathrm{2}}^ \star\) = 1.6 ± 0.6 μs, which is consistent within an order of magnitude with other DQD experimental results^{12,19} and theoretical estimates^{43,44,45} (see Supplementary Note 3) of the ergodic limit of the dephasing due to hyperfine coupling of the QD electron wave function with residual ^{29}Si. By measuring at faster timescales, an increased \(T_{\mathrm{2}}^ \star\) ~ 4 μs is observed. The absence of a magnetic field dependence suggests that the SO coupling does not contribute appreciably to \(T_{\mathrm{2}}^ \star\). Therefore, the \(T_{\mathrm{2}}^ \star\) observed at the MOS interface is consistent with expectations of the ^{29}Si enriched bulk Si, and there is no evidence of additional noise due to the MOS interface at this enrichment level.
Characterization of MOS charge noise
A second axis of coherent control for ST qubits is achieved through the tunable exchange coupling of the (1, 1) and (2, 0) charge states. This leads to hybridization between the (2, 0) and (1, 1) charge states and an exchange splitting, J(\(\epsilon\)), between the S and T_{0} qubit states that depends on detuning, \(\epsilon\) (Fig. 4a). By varying the strength of this interaction, we can achieve controlled coherent rotations, as demonstrated in Fig. 4b. Here, as described in ref. ^{46}, we initialize into a S(2, 0) ground state and then adiabatically separate the electrons into the (1, 1) charge configuration where J(\(\epsilon\)) is nearly zero and the qubit is initialized in the ground state of the SO field (\(\left { \uparrow \downarrow } \right\rangle\) or \(\left { \downarrow \uparrow } \right\rangle\)), a superposition of the S(1, 1) and T_{0}(1, 1) states. We apply a fast pulse to and from finite J(\(\epsilon\)) at \(\epsilon\) near 0 for some waiting time, which rotates the qubit state around the Bloch sphere about a rotation axis depending on both J and Δ_{SO}, the SOinduced splitting of the \(\left { \uparrow \downarrow } \right\rangle\) and \(\left { \downarrow \uparrow } \right\rangle\) states (Fig. 4a). For this experiment, we apply a field of 0.2 T along the [100] direction, which provides a small (0.5 MHz) residual Xrotation frequency. At detuning near \(\epsilon\) = 0, we observe an increased rotation frequency (Fig. 4c). As the exchange pulse moves to deeper detuning, we observe a decrease in rotation frequency as well as visibility. This is expected as J decreases and the rotation axis tilts towards the direction of the SO field difference.
Figure 4c shows the observed rotation frequency as a function of detuning. The rotation frequency can be expressed as \(\sqrt {J(\epsilon )^2 + {\mathit{\Delta }}_{{\mathrm{SO}}}^2}\), since the two components add in quadrature. Indeed, we see that at deep detuning the rotation frequency saturates near 0.5 MHz, due to the SO field at this magnetic field strength and orientation. Figure 4d shows the dephasing time, \(T_{\mathrm{2}}^ \star\), associated with coherent rotations at each detuning. Here we have extracted \(T_{\mathrm{2}}^ \star\) by fitting a Gaussian decay envelope \(( {{\mathrm{exp}}[ {  ( {t{\mathrm{/}}T_{\mathrm{2}}^ \star } )^2} ]} )\) to the rotations at each detuning point. Noise from charge fluctuations on the confinement gates causes deviations in the detuning point of the system, leading to dephasing of the qubit through changes in the rotation frequency. We measure shorter dephasing time near \(\epsilon\) = 0, which increases as we move to deeper detuning and eventually saturates at a few μs. We associate the saturation of \(T_{\mathrm{2}}^ \star\) at deeper detuning with the dominant noise mechanism transitioning from charge to magnetic noise due to residual background ^{29}Si. Following the method outlined in ref. ^{42}, we fit the rotation frequency to a smooth function to find the derivative, df(\(\epsilon\))/d\(\epsilon\). The ratio of \(T_{\mathrm{2}}^ \star\) to \(\left {{\mathrm{d}}f{\mathrm{/}}{\mathrm{d}}\epsilon } \right^{  1}\) gives a rootmeansquared charge noise of σ_{ ε } = 2 ± 0.6 μeV. This agreement with the best reported charge noise values in GaAs/AlGaAs and Si/SiGe material systems of a few μeV^{16,18,19,42,47} indicates that the polysilicon MOS device structure is a competitive material system with respect to the magnitude of quasistatic charge noise. Furthermore, successive measurements over the course of several weeks can be performed with no retuning of the device gate voltages, indicating that the MOS material system is an extremely stable qubit platform.
Improved decoherence can be achieved through dynamical decoupling (DD), which suppresses contributions from quasistatic noise through multirotation sequences that leverage time reversal symmetry. A schematic for a Hahnecho sequence to examine electrical noise is shown in Fig. 4e. As seen in Fig. 4f, a refocusing pulse can extend the qubit coherence with a \(T_{{\mathrm{2e}}}^{{\mathrm{echo}}}\) of 8.4 μs for a detuning, \(\epsilon\), where charge noise leads to \(T_{{\mathrm{2e}}}^ \ast\) = 1 μs. This is comparable to what has been observed in GaAs/AlGaAs^{42} and Si/SiGe^{12}. Likewise, Hahnecho techniques were able to improve decoherence from magnetic noise to a \(T_{{\mathrm{2m}}}^{{\mathrm{echo}}}\) of 70 μs (see Supplementary Note 3). These results illustrate our ability to extend coherence times through dynamical decoupling and unequivocally demonstrate full allelectrical control of the MOS SOdriven ST qubit.
Discussion
In previous implementations of ST qubits, dynamic nuclear polarization (DNP)^{48,49}, single nuclei^{20,21} and micromagnets^{19} have been used to create strong, stable difference in Zeeman splitting between two quantum dots to drive rotations. The SOdriven Xrotations presented here reach 20 MHz and limited primarily by preparation and readout constraints (see Supplementary Note 3). Though this is larger than what has been reported for a ST qubit in Si/SiGe using a micromagnet^{19}, it is smaller than the difference in Zeeman spin splitting of 50 to 1000 MHz between QDs reported in a number of other implementations mentioned above^{20,49,50}. Increased drive frequency with SO coupling is likely possible through a number of avenues. Increasing the vertical electric field (see Supplementary Note 1 and ref. ^{6}) and modifying the confinement potential (see Supplementary Note 1) will increase the strength of both the Rashba and Dresselhaus couplings. Additionally, the effect may be maximized by working with one of the QDs at higher occupation, since the two zvalleys at the heterointerface are predicted to have opposite sign of the Dresselhaus strength (see SM and refs. ^{6,27,28,30}). Single QDs have displayed a 140 MHz difference in ESR frequencies between electron occupations of N = 1 and N = 3 and electric field tunability^{6}, so drive frequencies of over 100 MHz seem realistic.
On the other hand, our study of the angular dependence shows that by orienting the magnetic fields perpendicular to the interface, the difference in gfactor between the QDs is minimized. This is important for spin–qubit platforms where spin splitting variation is detrimental (e.g., spin1/2 or exchange only qubits). This work also provides a theoretical foundation for the full angular dependence of an interface Dresselhaus and Rashba effect that avoids quantitative ambiguities due to gaugedependence. Future work also remains to establish how the microscopic details of the MOS interface affects the magnitudes of the Rashba and Dresselhaus terms.
Most significantly from this work, the SOdriven ST qubit is a sensitive probe of noise properties at the MOS interface. The \(T_{\mathrm{2}}^ \star\) of order 1–2 μs observed in the magnetic noise dominated regime is consistent with the ergodic limit expected from ^{29}Si (i.e. order of magnitude agreement). Charge noise magnitudes of 2 ± 0.6 μeV at T_{e} ~ 150 mK are observed and are comparable to other semiconductor systems. Overall, the MOS interface shows no indication of increased negative effects relative to qubit operation despite the imperfect dielectric/crystal interface. The opportunity to use MOS for highly sensitive spin coherent devices such as qubits has broad impact. Considering the possibilities for improvement and the reduced complexity in fabrication, the SOdriven ST qubit offers a promising implementation for quantum information technology.
Methods
DQD device and experimental setup
The DQD studied in this work was realized in a fully foundrycompatible (i.e. subtractive processing), singlegatelayer, isotopically enriched ^{28}Si MOS device structure. The material stack consists of 200 nm highly Arsenicdoped (5 × 10^{15} cm^{−2} at 50 keV) polysilicon and 35 nm of siliconoxide on top of a silicon substrate with an isotopically enriched epitaxial layer hosting 500 ppm residual ^{29}Si. Ohmic implants are formed using optical lithography and implantation of As at 3 × 10^{15} cm^{−2} at 100 keV. The confinement and depletion gates are defined by electron beam lithography followed by selective dry etching of the polysilicon. Phosphorus donors were implanted (4 × 10^{11} cm^{−2} at 45 keV) through a selfaligned implant window near the QD locations for alternative experiments^{20,21}. This was followed by an activation annealing process at 900 °C for 10 min in O_{2} and 5 min in N_{2} plus another 5 min in N_{2} at 1000 °C and a forming gas anneal at 400 °C.
Biasing the polysilicon gates confines a 2dimensional electron gas into quantum dot potentials. One QD is used as a single electron transistor (SET) remote charge sensor for spintocharge conversion. The rest of the device is tuned such that a DQD is formed, where one QD, define by the gate geometry, is tunnel coupled to a second, nonlithographic, QD formed nearby. This second QD, though unintended, survives thermal cycling and is a builtin feature of this device. The number of electrons in each QD is inferred from changes in current through the SET. Measurements were performed in a ^{3}He/^{4}He dilution refrigerator with a base temperature of around 8 mK. The effective electron temperature in the device was 150 mK. Fast RF lines we connected to cryogenic RC bias tees on the sample board, which to allow for the application of fast gate pulses. An external magnetic field was applied using a 3axis vector magnet. Additional information discussing the device and measurements is offered in the Supplementary Material and elsewhere^{5}.
Data availability
The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files. Additional data (e.g., source data for figures) are available from the corresponding author upon reasonable request.
References
Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in highpurity silicon. Nat. Mater. 11, 143–147 (2012).
Veldhorst, M. et al. An addressable quantum dot qubit with faulttolerant controlfidelity. Nat. Nano 9, 981–985 (2014).
Veldhorst, M. et al. A twoqubit logic gate in silicon. Nature 526, 410–414 (2015).
Gamble, J. K. et al. Valley splitting of singleelectron Si MOS quantum dots. Appl. Phys. Lett. 109, 253101 (2016).
Rochette, S. et al. Singleelectronoccupation metaloxidesemiconductor quantum dots formed from efficient polysilicon gate layout. Preprint at http://arxiv.org/abs/1707.03895 (2017).Ne
Veldhorst, M. et al. Spinorbit coupling and operation of multivalley spin qubits. Phys. Rev. B 92, 201401 (2015).
Jones, C. et al. A logical qubit in a linear array of semiconductor quantum dots. Preprint at http://arxiv.org/abs/1608.06335 (2016).
Ralls, K. S. et al. Discrete resistance switching in submicrometer silicon inversion layers: individual interface traps and lowfrequency 1/f noise. Phys. Rev. Lett. 52, 228–231 (1984).
Culcer, D. & Zimmerman, N. M. Dephasing of si singlettriplet qubits due to charge and spin defects. Appl. Phys. Lett. 102, 232108 (2013).
Bermeister, A., Keith, D. & Culcer, D. Charge noise, spinorbit coupling, and dephasing of singlespin qubits. Appl. Phys. Lett. 105, 192102 (2014).
Kawakami, E. et al. Electrical control of a longlived spin qubit in a Si/SiGe quantum dot. Nat. Nano 9, 666–670 (2014).
Eng, K. et al. Isotopically enhanced triplequantumdot qubit. Sci. Adv. 1, e1500214 (2015).
Zajac, D. M., Hazard, T. M., Mi, X., Wang, K. & Petta, J. R. A reconfigurable gate architecture for si/sige quantum dots. Appl. Phys. Lett. 106, 223507 (2015).
Mi, X., Péterfalvi, C. G., Burkard, G. & Petta, J. R. Highresolution valley spectroscopy of si quantum dots. Phys. Rev. Lett. 119, 176803 (2017).
Schoenfield, J. S., Freeman, B. M. & Jiang, H. Coherent manipulation of valley states at multiple charge configurations of a silicon quantum dot device. Nat. Commun. 8, 64 (2017).
Thorgrimsson, B. et al. Extending the coherence of a quantum dot hybrid qubit. npj Quantum Inf. 3, 32 (2017).
Borselli, M. G. et al. Pauli spin blockade in undoped si/sige twoelectron doublequantum dots. Appl. Phys. Lett. 99, 063109 (2011).
Shi, Z. et al. Coherent quantum oscillations and echo measurements of a si charge qubit. Phys. Rev. B 88, 075416 (2013).
Wu, X. et al. Twoaxis control of a singlet–triplet qubit with an integrated micromagnet. Proc. Natl Acad. Sci. USA 111, 11938–11942 (2014).
HarveyCollard, P. et al. Coherent coupling between a quantum dot and a donor in silicon. Nat. Commun. 8, 1029 (2017).
Rudolph, M. et al. Coupling MOS quantum dot and phosphorous donor qubit systems. 2016 IEEE Int. Electron Dev. Meet. 34.1.1–34.1.4 (2016).
Rössler, U. & Kainz, J. Microscopic interface asymmetry and spinsplitting of electron subbands in semiconductor quantum structures. Solid State Commun. 121, 313–316 (2002).
Golub, L. E. & Ivchenko, E. L. Spin splitting in symmetrical sige quantum wells. Phys. Rev. B 69, 115333 (2004).
Nestoklon, M. O., Golub, L. E. & Ivchenko, E. L. Spin and valleyorbit splittings in SiGeSi heterostructures. Phys. Rev. B 73, 235334 (2006).
Prada, M., Klimeck, G. & Joynt, R. Spin–orbit splittings in si/sige quantum wells: from ideal Si membranes to realistic heterostructures. New J. Phys. 13, 013009 (2011).
Nestoklon, M. O., Ivchenko, E. L., Jancu, J.M. & Voisin, P. Electric field effect on electron spin splitting in SiGeSi quantum wells. Phys. Rev. B 77, 155328 (2008).
Ferdous, R., et al. Valley dependent anisotropic spin splitting in silicon quantum dots. Preprint at http://arxiv.org/abs/1702.06210 (2017).
Ferdous, R., et al. Interface induced spinorbit interaction in silicon quantum dots and prospects of scalability. Preprint at http://arxiv.org/abs/1703.03840 (2017).
Huang, W., Veldhorst, M., Zimmerman, N. M., Dzurak, A. S. & Culcer, D. Electrically driven spin qubit based on valley mixing. Phys. Rev. B 95, 075403 (2017).
Ruskov, R., Veldhorst, M., Dzurak, A. S. & Tahan, C. Electron gfactor of valley states in realistic silicon quantum dots. Preprint at http://arxiv.org/abs/1708.04555 (2017).
Alekseev, P. S. & Nestoklon, M. O. Effective oneband approach for the spin splittings in quantum wells. Phys. Rev. B 95, 125303 (2017).
Botzem, T. et al. Quadrupolar and anisotropy effects on dephasing in twoelectron spin qubits in GaAs. Nat. Commun. 7, 11170 (2016).
Fujita, T., Baart, T. A., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent shuttle of electronspin states. npj Quantum Inf. 3, 22 (2017).
Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 (2016).
Manchon, A., Koo, H. C., Nitta, J., Frolov, S. M. & Duine, R. A. New perspectives for Rashba spinorbit coupling. Nat. Mater. 14, 871–882 (2015).
Soumyanarayanan, A., Reyren, N., Fert, A. & Panagopoulos, C. Emergent phenomena induced by spin–orbit coupling at surfaces and interfaces. Nature 539, 509–517 (2015).
Lidar, D. A., Chuang, I. L. & Whaley, K. B. Decoherencefree subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998).
HarveyCollard, P. et al. Highfidelity singleshot readout for a spin qubit via an enhanced latching mechanism. Preprint at http://arxiv.org/abs/1703.02651 (2017).
Yang, C. H. et al. Spinvalley lifetimes in a silicon quantum dot with tunable valley splitting. Nat. Commun. 4, 2069 (2013).
Tahan, C. & Joynt, R. Relaxation of excited spin, orbital, and valley qubit states in ideal silicon quantum dots. Phys. Rev. B 89, 075302 (2014).
Hwang, J. C. C. et al. Impact of gfactors and valleys on spin qubits in a silicon double quantum dot. Phys. Rev. B 96, 045302 (2017).
Dial, O. E. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlettriplet qubit. Phys. Rev. Lett. 110, 146804 (2013).
Assali, L. V. C. et al. Hyperfine interactions in silicon quantum dots. Phys. Rev. B 83, 165301 (2011).
Witzel, W. M., Rahman, R. & Carroll, M. S. Nuclear spin induced decoherence of a quantum dot in si confined at a sige interface: Decoherence dependence on ^{73}Ge. Phys. Rev. B 85, 205312 (2012).
Witzel, W. M., Carroll, M. S., Cywiński, L. & Das Sarma, S. Quantum decoherence of the central spin in a sparse system of dipolar coupled spins. Phys. Rev. B 86, 035452 (2012).
Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).
Petersson, K., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a oneelectron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).
Foletti, S., Bluhm, H., Mahalu, D., Umansky, V. & Yacoby, A. Universal quantum control of twoelectron spin quantum bits using dynamic nuclear polarization. Nat. Phys. 5, 903–908 (2009).
Nichol, J. M. et al. Highfidelity entangling gate for doublequantumdot spin qubits. npj Quantum Inf. 3, 3 (2017).
Takeda, K. et al. A faulttolerant addressable spin qubit in a natural silicon quantum dot. Sci. Adv. 2, e1600694 (2016).
Acknowledgements
We would like to thank Rusko Ruskov for discussions. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract DEAC5206NA25396) and Sandia National Laboratories (Contract DENA0003525). Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the DOE’s National Nuclear Security Administration under contract DENA0003525.
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R.M.J, P.H.C., and M.S.C. designed the experiments. R.M.J. performed the central measurements and analysis presented in this work. P.H.C. performed supporting measurements on a similar device that establish repeatability of observations. N.T.J. developed the theoretical description of the results with the help of A.M.M., V.S., J.K.G., A.D.B., and W.M.W. providing critical insights. R.M.J., M.S.C., N.T.J., P.H.C., A.M.M., and M.R. analyzed and discussed central results throughout the project. D.R.W., J.A., R.P.M., J.R.W., T.P., and M.S.C. designed the process flow, fabricated devices, and designed/characterized the ^{28}Si material growth for this work. J.R.W. provided critical nanolithography steps. M.S.C. supervised the combined effort, including coordinating fabrication and identifying modeling needs for the experimental path. R.M.J. and M.S.C. wrote the manuscript with input from all coauthors.
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Jock, R.M., Jacobson, N.T., HarveyCollard, P. et al. A silicon metaloxidesemiconductor electron spinorbit qubit. Nat Commun 9, 1768 (2018). https://doi.org/10.1038/s41467018042000
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DOI: https://doi.org/10.1038/s41467018042000
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