Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
Conditions for Equivalent Noise Sensitivity of Geometric and Dynamical Quantum Gates
复制标题
DOI：
10.1103/prxquantum.3.030310
复制
发表时间：
2022-07-19
期刊：
影响因子：
9.7
通讯作者：
Kestner, J. P.
中科院分区：
文献类型：
--
作者：
Colmenar, R. K. L.;Gungordu, Utkan;Kestner, J. P.
人们通常期望几何量子门比动态门对某些类型的错误具有更强的弹性，这使得它们成为鲁棒量子计算的理想选择。然而，由于文献中看似相互矛盾的结果，这一点仍有争议。在这里，我们将动态不变理论与滤波器函数结合使用，以便分析表征任意量子门的噪声灵敏度。对于产生几何门的任何控制哈密顿量，我们发现，在某些常见条件下，可以构造另一种控制哈密顿量，该控制哈密顿量产生具有相同噪声灵敏度（由滤波器函数表征）的等效动态门。我们的结果适用于任意维度的希尔伯特空间，但我们通过检查实验相关的单量子位场景并提供等效几何和动态门的明确示例来说明我们的结果。
Geometric quantum gates are often expected to be more resilient than dynamical gates against certain types of error, which would make them ideal for robust quantum computing. However, this is still up for debate due to seemingly conflicting results in the literature. Here we use dynamical invariant theory in conjunction with filter functions in order to analytically characterize the noise sensitivity of an arbitrary quantum gate. For any control Hamiltonian that produces a geometric gate, we find that, under certain common conditions, one can construct another control Hamiltonian that produces an equivalent dynamical gate with identical noise sensitivity (as characterized by the filter function). Our result holds for a Hilbert space of arbitrary dimensions, but we illustrate our result by examining experimentally relevant singlequbit scenarios and providing explicit examples of equivalent geometric and dynamical gates.