Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.

中文翻译：

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通过绝热捷径对非绝热几何门进行数字量子模拟


几何相位用于构造量子门，因为它天然地抵抗局部噪声，充当几何量子计算的模块化单元。同时，需要快速非绝热几何门来减少退相干引起的信息损失。在这里，我们提出了根据绝热捷径（STA）对非绝热几何量子门进行数字模拟。更具体地说，我们将基于不变性的逆向工程与最优控制理论相结合，在两级量子位系统的背景下设计快速且鲁棒的阿贝尔几何门以对抗系统误差。我们以 X 门和 T 门为例，通过理想量子电路中的模拟来评估保真度和鲁棒性。我们的结果还可以扩展到构建两个量子位门，例如受控相位门，它共享等效的有效哈密顿量，并绕单个量子位的 Z 轴旋转。这些受STA启发的非绝热几何门可以在物理上实现量子纠错，从而在嘈杂的中尺度量子（NISQ）时代实现容错量子计算。