Scalable Gate Architecture for a One-Dimensional Array of Semiconductor Spin Qubits

We demonstrate a 12-quantum-dot device fabricated on an undoped Si/SiGe heterostructure as a proof of concept for a scalable, linear gate architecture for semiconductor quantum dots. The device consists of nine quantum dots in a linear array and three single-quantum-dot charge sensors. We show reproducible single-quantum-dot charging and orbital energies, with standard deviations less than 20% relative to the mean across the nine-dot array. The single-quantum-dot charge sensors have a charge sensitivity of $8.2\times {10}^{-4}e/\sqrt{\mathrm{Hz}}$ and allow for the investigation of real-time charge dynamics. As a demonstration of the versatility of this device, we use single-shot readout to measure the spin-relaxation time $T_1=170\mathrm{ms}$ at a magnetic field $B=1\mathrm{T}$. By reconfiguring the device, we form two capacitively coupled double quantum dots and extract a mutual charging energy of $200\mu \mathrm{eV}$, which indicates that 50-GHz two-qubit gate-operation speeds are feasible.

Figure 1

(a) False-color scanning-electron-microscope image of the overlapping gate architecture. A linear array of nine quantum dots is formed under plunger gates $P1,P2,\dots ,P9$. Tunnel couplings are controlled using barrier gates $B1,B2,\dots ,B10$. Quantum-dot charge sensors are formed under gates $S1,S2$, and $S3$. (b) (Lower panel) comsol simulation of the electron density, $n$, in the quantum well. (Upper panel) The confinement potential, $V(x)$, along the dashed line in the lower panel.

Figure 2

(a) Charge-stability diagram of quantum dot 9. The derivative of charge-sensor-dot-3 conductance, $d{g}_{S3}/d{V}_{P9}$, plotted as a function of $V_{P9}$ and $V_{B10}$. For low voltages, dot 9 is emptied of free electrons, reaching the $N_9=0$ charge state. (b) The addition energy, $E_{\mathrm{add}}$, plotted as a function of electron number $N$ for dots 4, 6, 8, and 9. (c) Pulsed-gate spectroscopy. The effective tunneling rate onto the dot is dependent on $V_{\text{pulse}}$. (d) An orbital excited state with energy $E_{\mathrm{orb}}=\alpha V_{\mathrm{orb}}=3.4\mathrm{meV}$ is visible in dot 9.

Figure 3

(a) A Coulomb-blockade peak is visible in sensor-dot-3 conductance, $g_{S3}$, which is plotted as a function of the gate voltages $V_{P8}$ and $V_{S3}$. (b) $g_{S3}$ measured at the locations indicated by the dashed lines in (a). The Coulomb-blockade peak shifts by $\mathrm{\Delta }{V}_{S3}=0.26\mathrm{mV}$ when $N_8$ changes by one electron. (c) $\mathrm{\Delta }{V}_{S3}$ is measured for dots 2–8 and plotted as a function of the distance $d$ from the sensor dot. The black line is the theoretical prediction. (d) The approximately $1/d^3$ power-law dependence is qualitatively understood as the field of a dipole formed by the electron in the quantum well (the blue circle) and its positive image charge (the red circle).

Figure 4

(a) The current, $I$, through sensor dot 3, plotted as a function of $V_{P8}$ and time, $t$, near the $N_8=0$ to 1 charge transition. (b) Time series extracted from the data in (a) at the positions shown by the dashed lines. The dwell time in the $N_8=1$ charge state increases as $V_{P8}$ is made more positive. The traces are offset by 2 nA for clarity. (c) Time-averaged quantum-dot-8 occupation, $⟨N_8⟩$, extracted from the data in (a) and plotted as a function of $V_{P8}$. The data are fit to a Fermi function $f(E)$.

Figure 5

(a) A time series of the current, $I$, through sensor dot 3, with dot 8 configured at the $N_8=0$ to 1 charge transition. (b) A histogram of a 1-s time series exhibits two Gaussian peaks with width ${\sigma }_I=0.112\mathrm{nA}$ separated by an amount $\mathrm{\Delta }I=0.772\mathrm{nA}$. (c) The $\mathrm{SNR}=\mathrm{\Delta }I/{\sigma }_I$ plotted as a function of the filter cutoff frequency, $f$ (the black crosses). The data fall between the expected SNR for a current level of 4 nA (blue) and 6 nA (red) based on the measured noise spectra at each current level, shown in the inset.

Figure 6

Single-shot spin measurements. (a) Electron density $n$ in the quantum well showing the configuration used to perform readout on dot 8. (b) A single-electron spin is measured by aligning the spin states such that a spin-up electron (the red level) can tunnel off of the dot and be replaced by a spin-down electron, while a spin-down electron (the blue level) does not have sufficient energy to tunnel off of the dot. (c) Example single-shot traces acquired at $B=1\mathrm{T}$. The vertical dashed line at $t=5\mathrm{ms}$ marks the beginning of the readout phase. Red (blue) traces correspond to spin-up (spin-down) electrons. Spin-up events result in a “spin bump.” (d) $P_{\uparrow }$ decays exponentially with $t_{\mathrm{wait}}$, with a best fit $T_1=170\pm 17\mathrm{ms}$.

Figure 7

Dots 6 and 7, and dots 8 and 9, are simultaneously tuned up to form two DQDs, as shown by the charge-stability diagrams in (a),(b). (c) The capacitive interaction between the two DQDs is extracted by measuring the quadruple-dot charge-stability diagram as a function of ${ϵ}_L$ and ${ϵ}_R$. The $(N_6,N_7)=(1,0)$ to (0, 1) interdot charge transition shifts by $\mathrm{\Delta }{ϵ}_L=0.77\mathrm{mV}$ when ${ϵ}_R$ is swept across the $(N_8,N_9)=(1,0)$ to (0, 1) interdot charge transition.