Universal Robust Quantum Gates via Doubly Geometric Control

Abstract

Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources remains a long-standing limitation, particularly in realistic large-scale circuits with complex noise environments. This limitation is largely due to the absence of a general framework that directly characterizes error accumulation and enables systematic improvement. Here we establish such a framework for universal doubly geometric gates by embedding target operations into a hierarchy of level-n identity constructions. This approach enables direct quantification of error accumulation while removing structural constraints inherent in previous schemes. We analytically show that the defining conditions lead to simultaneous fourth-order suppression of control errors, with a systematic extension to sixth-order suppression via higher-level constructions. Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates, with potential implications for fault-tolerant quantum information processing.

Figures (3)

• Figure 1: Comparison of the $S$ gate error curves for (a) and (b) dynamical scheme ZhengShiBiao_PRA_2016SM_UDOG, (c) and (d) non-cyclic NGQC scheme ChenTao_PRApplied_2024, (e) and (f) traditional NGQC scheme ZhaoPengZhi_2017XuYun_PRL_2020, and (g) and (h) level-3 UDOG scheme. The left and right columns correspond to the detuning ($\delta$) and Rabi ($\epsilon$) errors, respectively. The optimal parameters used here are $\left(\xi_{1}=1.5, \xi_{2}=1\right)$, and the pulse shapes used here are square. Error distances $d$ for panels (a)–(h) are: (a), (b) $\{3.46, 2.72\}$;(c), (d) $\{3.02, 2.26\}$; (e), (f) $\{3.70, 2.40\}$; and (g), (h) $\{0, 0\}$.
• Figure 2: Gate fidelity of the level-3 $S$ gate as a function of (a) detuning error $\delta$ and (b) Rabi error $\epsilon$. The optimal parameters are $\left(\xi_{1}=1.5,\xi_{2}=1\right)$, and the pulse shapes used here are square. (c) and (d) represent the corresponding filter functions Green.13.
• Figure 3: Gate fidelity in the superconducting transmon qubits. (a) corresponds the level-3 identity $S$ gate, and (b) the CPHASE gate, where the tunable parameters used here are $\left(\xi_{1}=1.5,\xi_{2}=1\right)$. (c) and (d) correspond to the $X$ and iSWAP gate considering the $ZZ$ crosstalk error $\delta_{zz}$ ($\delta_{zz}^{\prime}$), where the tunable parameters used here are $\left(\xi_{1}=-5/3,\xi_{2}=5/3\right)$.