Accelerated Adiabatic Passage of a Single Electron Spin Qubit in Quantum Dots

Adiabatic processes can keep the quantum system in its instantaneous eigenstate, which is robust to noises and dissipation. However, it is limited by sufficiently slow evolution. Here, we experimentally demonstrate the transitionless quantum driving (TLQD) of the shortcuts to adiabaticity in gate-defined semiconductor quantum dots (QDs) to greatly accelerate the conventional adiabatic passage for the first time. For a given efficiency of quantum state transfer, the acceleration can be more than twofold. The dynamic properties also prove that the TLQD can guarantee fast and high-fidelity quantum state transfer. In order to compensate for the diabatic errors caused by dephasing noises, the modified TLQD is proposed and demonstrated in experiment by enlarging the width of the counterdiabatic drivings. The benchmarking shows that the state transfer fidelity of 97.8% can be achieved. This work will greatly promote researches and applications about quantum simulations and adiabatic quantum computation based on the gate-defined QDs.

Figure 1

The device and its basic properties. (a) The false-colored micrograph of the device. The high-frequency pulses are applied through the plunger gates $P1$ and $P2$, and the MW driving is connected with $P1$. (b) Charge stability diagram around single electron region. The position of $I$, $B$, and $O$ are represented by the green star, black square, and blue circle, respectively. The position of the initialization is also used for the readout. (c) The schematic of TLQD. (d) Rabi frequency $f_{\text{Rabi}}$ as a function of the MW amplitude. Its maximum value is about $f_{\text{Rabi}}^{\max }\sim 7.5\mathrm{MHz}$.

Figure 2

The result of TLQD. (a) The final spin-down probability $P_{\downarrow }$ as a function of the evolution time $T_e$ using the conventional adiabatic evolution and TLQD. The red solid line is the fitting to the formula $A{P}_{\downarrow }^{\mathrm{LZ}}+B$, giving the value of ${\mathrm{\Omega }}_R/2\pi =4.63\mathrm{MHz}$. The inset displays the speedup factor $\eta$ as functions of $P_{\downarrow }$ and the efficiency of state transfer $F_{\mathrm{flip}}$. (b) The simulation results of $P_{\downarrow }$ and $F_{\mathrm{flip}}$ as a function of $T_e$ under different variance of qubit frequency noise $\sigma \sim 0.0$ (green solid line), 3.5 (red dashed line), and 7.0 MHz (black dash-dotted line). To better compare the simulation and experimental results, the red dashed line with $\sigma \sim 3.5\mathrm{MHz}$ is also plotted in (a). The modulation depth is ${\delta }_d=100.0\mathrm{MHz}$. The maximum Rabi frequency is assumed to be $f_{\text{Rabi}}^{\max }=7.5\mathrm{MHz}$. (c) and (d) are the experimental and simulation results of the dynamics of $P_{\downarrow }$, respectively. The Rabi frequency is ${\mathrm{\Omega }}_R/2\pi =4.18\mathrm{MHz}$.

Figure 3

The result of MODTLQD. (a) The enhancement of spin flip probability $\mathrm{\Delta }{P}_{\downarrow }$ as a function of $\alpha$ under different $T_e$. The markers are experimental data, and the lines represent simulation results. The variance of qubit frequency is $\sigma \sim 2.9\mathrm{MHz}$. The traces are shifted vertically for clarity. (b) The enhancement of spin flip probability $\mathrm{\Delta }{P}_{\downarrow }^{\prime }$ as a function of $T_e$. The width factor is set to be $\alpha =2.5$. The Rabi frequency in (a) and (b) is ${\mathrm{\Omega }}_R/2\pi \sim 4.0\mathrm{MHz}$. (c) The benchmarking of the efficiency of state transfer using the MODTLQD, giving the value of $p=0.978\pm 0.01$. The inset corresponds to the result of conventional adiabatic evolution, which has the oscillation instead of an exponential decay. (d) The schematic of pulse sequences to benchmark the spin flip fidelity.