Suppressing classical noise in the accelerated geometric phase gate by optimized dynamical decoupling

In the quantum-computation scenario, the geometric phase gates are becoming increasingly attractive for their intrinsic fault tolerance to disturbance. With an adiabatic cyclic evolution, Berry phase appears to realize a geometric transformation. Performing the quantum gates as many as possible within the timescale of coherence, however, remains an inconvenient bottleneck due to the systematic errors. Here we propose an accelerated adiabatic quantum gate based on the Berry phase, the transitionless driving, and the dynamical decoupling. It reconciles a high fidelity with a high speed in the presence of control noise or imperfection. We optimize the dynamical-decoupling sequence in the time domain under a popular Gaussian noise spectrum following the inversely quadratic power law.

Figure 1

The population dynamics of the qubit on $|+\rangle$ under various Hamiltonians, in units of the Rabi frequency ${\mathrm{\Omega }}_R$. The parameters are set as ${\omega }_a=100\pi$ MHz, ${\omega }_b=60\pi$ MHz, and ${\mathrm{\Omega }}_R=20\pi$ MHz.

Figure 2

Landscape of the gate fidelity ${\mathcal{F}}_B$ under the stochastic $B_0$ in the parameter space of the strength-memory ratio $\mathrm{\Gamma }/\gamma$ and the running period $\gamma T$.

Figure 3

Landscape of the gate fidelity ${\mathcal{F}}_{\varphi }$ under the stochastic $\dot{\varphi }$ in the parameter space of the strength-memory ratio $\mathrm{\Gamma }/\gamma$ and the running period $\gamma T$. In (a) and (b), the noise-free parameter $\theta$ is set as $\theta \left(t\right)=\omega t$ and $\theta \left(t\right)=\omega t-sin\left(\omega t\right)$, respectively.

Figure 4

Landscape of the spin-echo gate fidelity ${\mathcal{F}}_{\mathrm{SE}}$ under the stochastic $B_0$ in the parameter space of the strength-memory ratio $\mathrm{\Gamma }/\gamma$ and the running period $\gamma T$.

Figure 5

The gate fidelity under various DD sequences (SE, $\mathrm{CPMG}n$, and $\mathrm{UDD}n$) in the presence of the Gaussian noise following the inverse-quadratic power-law spectrum. (a) The gate dynamics versus $\gamma T$ when $\mathrm{\Gamma }/\gamma =4$; (b) the gate dependence on $\mathrm{\Gamma }/\gamma$ when $\gamma T=4$.