Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits. We discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk for instantaneous spectral diffusion (ISD). Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary single-qubit gates of $2.1\times {10}^{-4}$ when ISD is not considered and $3.4\times {10}^{-4}$ when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from $5\times {10}^{-4}\to 3\times {10}^{-3}$ over a broad range of dipole-dipole interaction strengths.

中文翻译：

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为稀土离子掺杂晶体中的单离子量子计算设计门操作

如果单个离子可以用作量子位，则基于稀土离子掺杂晶体的量子计算机在可扩展性和连接性方面显示出有希望的特性。通过模拟，我们研究了此类量子位上的门操作。我们讨论门和系统参数如何影响门误差、每个量子位所需的频率带宽以及瞬时谱扩散 (ISD) 的风险。此外，我们研究了系统参数的不确定性如何影响门误差，以及系统需要知道的精确程度。我们发现任意单量子比特门的门错误$2.1\times {10}^{-4}$ 当不考虑 ISD 和 $3.4\times {10}^{-4}$当我们注意将其最小化时。此外，我们构建了两个量子比特门，其误差范围为$5\times {10}^{-4}\to 3\times {10}^{-3}$ 在广泛的偶极-偶极相互作用强度范围内。