Engineered Robustness for Nonadiabatic Geometric Quantum Gates

TL;DR

The work develops a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that explicitly suppresses dynamical contamination through an auxiliary robustness constraint, achieving super-robust single-qubit gates against driving-amplitude fluctuations. It extends NGQG design to open, noncyclic paths to gain design flexibility and demonstrates high-fidelity single-qubit gates on superconducting transmons, with fidelity scaling $F=1-\mathcal{O}(\varepsilon^4)$ under Rabi errors. The study further analyzes two-qubit NGQGs under parametric driving, identifying intrinsic fidelity limits and practical fragilities arising from phase compensation and waveform calibration, thereby informing future control strategies for scalable geometric quantum computation. Overall, the framework is simple, broadly applicable across platforms, and offers a physically grounded design approach that complements numerical optimization for high-fidelity, noise-resilient quantum gates.

Abstract

While geometric quantum gates are often theorized to possess intrinsic resilience to control errors by exploiting the global properties of evolution paths, this promise has not consistently translated into practical robustness. We present a streamlined framework for nonadiabatic geometric quantum gates (NGQGs) that incorporates additional auxiliary constraints to suppress dynamical contamination and achieve super-robust performance. Within this framework, we also design NGQGs using noncyclic paths, offering enhanced design flexibility. Implemented on superconducting transmon qubits, our scheme realizes high-fidelity single-qubit gates that are robust against Rabi amplitude error $ε$, with infidelity scaling as $\mathcal{O}(ε^4)$, in contrast to the $\mathcal{O}(ε^2)$ behavior of conventional dynamical gates. We further analyze two-qubit NGQGs under parametric driving. Our results identify subtle limitations that compromise performance in two-qubit scenarios, underscoring the importance of phase compensation and waveform calibration. The demonstrated simplicity and generality of our super-robust NGQG scheme make it applicable across diverse quantum platforms.

Figures (4)

• Figure 1: The trajectories of the auxiliary state $|\xi_1(t)\rangle$ on the Bloch sphere for an $X$ gate realized by three different NGQG schemes: (a) NGQG_P1, (b) NGQG_P2, and (c) SR-NGQG. NGQG_P1 and NGQG_P2 are adopted from ngqcChen2018. The blue and yellow curves correspond to Rabi errors of $\epsilon=0$ and 0.1, respectively. Notice that the SR-NGQG scheme uses an open path. The NQQGs in (a) and (c) exhibit robustness against Rabi error, as indicated by the relatively small change in their trajectories under error perturbation. In contrast, the NGQG in (b) is not robust, showing a pronounced trajectory shift in the presence of Rabi error. A detailed comparison of their robustness performance is given in Fig.\ref{['robust']}.
• Figure 2: QPT and RB characterization of single-qubit gates realized by our SR-NGQG scheme. (a) Bar charts show the real and imaginary parts of the reduced quantum process matrices $\chi$ for four gates: $X$, $Y$, $X/2$, and $Y/2$, respectively. The solid black outlines are for ideal gates. QPT fidelity is calculated using the experimental data: 0.996($X$), 0.994($Y$), 0.991($X/2$), and 0.993($Y/2$). (b) Sequence fidelity as a function of the number of Clifford gates for both the reference and interleaved RB experiments. Each data point is averaged over 50 random sequences, with the standard deviations plotted as error bars. Fitting the reference curve gives an average gate fidelity of 0.9981 for the single-qubit gates. Fidelity of the four specific gates, $X$, $Y$, $X/2$, and $Y/2$ can be extracted from the difference between the reference and the interleaved curves.
• Figure 3: QPT Fidelity as a function of Rabi error for four single-qubit gates. (a)&(b) $X$ and $Y$ gates implemented using our SR-NGQG scheme, NGQG_P1, NGQG_P2, SSSP pulse, and a dynamical gate of a Gaussian pulse. (c)&(d) $X/2$ and $Y/2$ gates realized using SR-NGQG, NGQG_P1, NGQG_P2, and a dynamical gate of a Gaussian pulse.
• Figure 4: Numerical simulations of two-qubit NGQGs in the rotating frame defined in the main text, using . Panels (a) and (b) show the temporal evolution of state populations (upper) and evolution operators (lower) for iSWAP and CZ gates, respectively. Small oscillations observed in the population is due to off-resonant terms in the Hamiltonian of Eq. (\ref{['twoQHrotating']}). Gate fidelity is calculated using $\mathrm{Tr}(\tfrac{1}{4}U_\text{exp}U_\text{ideal}^\dagger)$, yielding 99.3% (iSWAP) and 99.6% (CZ). (c) Fidelity of three gates as a function of $\Delta A$, fluctuations in the amplitude of parametric driving. The equivalent Rabi error is calculated as $g_{12}J_1(A/\Delta)$.