Conveyor-mode electron shuttling through a T-junction in Si/SiGe

Abstract

Conveyor-mode shuttling in gated Si/SiGe devices enables adiabatic transfer of single electrons, electron patterns and spin qubits confined in quantum dots across several microns with a scalable number of signal lines. To realize their full potential, linear shuttle lanes must connect into a two-dimensional grid with controllable routing. We introduce a T-junction device linking two independently driven shuttle lanes. Electron routing across the junction requires no extra control lines beyond the four channels per conveyor belt. We measure an inter-lane charge transfer fidelity of $F = 100.0000000^{+0}_{-9\times 10^{-7}}\,\%$ at an instantaneous electron velocity of $270\,\mathrm{mm}\,\mathrm{s}^{-1}$. The filling of 54 quantum dots is controlled by simple atomic pulses, allowing us to swap electron patterns, laying the groundwork for a native spin-qubit SWAP gate. This T-junction establishes a path towards scalable, two-dimensional quantum computing architectures with flexible spin qubit routing for quantum error correction.

Figures (11)

• Figure 1: T-junction device and atomic pulses.a False color scanning electron micrograph of the surface of a device nominally identical to the device measured, including gate labels. Gate color coding is consistent between all sub-figures and indicates gates comprising gate sets $\mathrm{S}_{\mathrm{x}, i}$ and $\mathrm{S}_{\mathrm{y}, i}$ (see methods). The scale bar is 5µm. b Atomic pulses for charge initialization and readout. The indicated voltages are typical values. Typical values are $t_{\mathrm{S}} \approx$ 10ms and $t_{\mathrm{RO}} \approx$ 100ms. c Horizontal and vertical charge shuttle atomic pulses. The first half of $\lambda_x^1$, up to the dashed line, describes $\lambda_{\mathrm{L}\rightarrow\mathrm{R}}$. d Junction transfer atomic pulse. Pulses for finger gates in x- and y-shuttle are shown on the bottom and top, respectively. Note that the x- and y-shuttle are not operated simultaneously. e Commonly used composite pulses. R: destructive readout pulse. ROI: readout and initialization calibration pulse. f Nominal dot positions in the idle state. In the readout state (see methods), all $\mathrm{QD\;X}_{n}$ are shifted two gates towards the right. Periodic continuation of more $\mathrm{QDs}$ are omitted but indicated with (//) symbols. g Simulated potentials $\varphi$ and electron ground state probability densities (yellow-red circular shapes) at three positions in the device corresponding to three points in time. Claviature gates are shown as outlines and screening gates are indicated as a light gray grid. Blue arrows: Electron states in $\mathrm{QD\;X}_{16}$ and $\mathrm{QD\;Y}_{0}$ in the idle state. Red arrow: Electron during inter-lane junction transfer, time indicated by blue dashed line in (d). 95%, 68%, 1% probability density levels shown in yellow, orange and red, respectively. (time-dependence of simulations in Supplementary Movies 1 and 2)
• Figure 1: Junction transfer atomic pulse $\lambda^1_\mathrm{JL}$ This figure follows the legend in INCOMPLETE REFERENCE. The atomic pulse shown shuttles the charge in $\mathrm{QD\;X}_{18}$ to $\mathrm{QD\;Y}_{0}$.
• Figure 1: Additional simulation results for $A=$ 260mV and $A=$ 100mV.$A_\mathrm{x} = A_\mathrm{y}= A_\mathrm{J} = A$. a, e Expectation value of electron x and y position in the ground state. b, f Orbital splitting and wavefunction projection during transfer. Blue markers indicate the time steps shown in (d, h), respectively. c, g Corresponding applied voltage pulses. Colors follow the gate color-coding in INCOMPLETE REFERENCE. d First excited states for the time steps shown in (b), corresponding to time steps shown in INCOMPLETE REFERENCEg. Teal, green and blue sequence correspond to the $95\,\%$, $68\,\%$, $1\,\%$ levels of the probability density for the first excited state. h Ground states and first excited states for the time steps shown in (f). 95%, 68%, 1% probability density levels of the ground states shown in yellow, orange and red, respectively. First excited states follow color map in (d).
• Figure 2: Verifying shuttling in the x- and y-shuttles. Applied pulses and readout histograms with one and zero electrons loaded, the latter as reference pulse. Branching notation in the pulses indicate that the whole pulse is repeated once for each branch, with the exception of the ROI-pulse separated by dashed lines, which is only performed for the first branch repetition. Histograms show the sum of $\mathrm{QD\;X}_{0}$ occupancy readout counts separated for the pulse branches with either one electron or zero electrons loaded. The $\mathrm{QDs}$ along the shuttle paths are shown next to the legends. $n_\mathrm{total} = 1000$, $A_\mathrm{x} = A_\mathrm{y} = A_\mathrm{J} =$ 260mV and $v_\lambda = v_\mathrm{J} =$ 270mms for all measurements. Results for $v_\lambda = v_\mathrm{J} =$ 28mms shown in INCOMPLETE REFERENCE. a Shuttling in the x-shuttle. b Shuttling in the x-shuttle up to $\mathrm{QD\;X}_{17}$ followed by y-shuttle.
• Figure 2: Verifying shuttling in the x- and y-shuttles. Complementary results of INCOMPLETE REFERENCE at $v_\lambda = v_\mathrm{J} =$ 28mms. a Shuttling in the x-shuttle. b Shuttling in the x-shuttle up to $\mathrm{QD\;X}_{17}$ followed by the y-shuttle.