论文标题
与高斯电路的Gottesman-Kitaev-Preskill国家有效模拟
Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits
论文作者
论文摘要
我们研究了Gottesman-Kitaev-Preskill（GKP）状态的经典模拟性与任意位移，一系列符号操作和同胞测量。对于这些类型的电路，不能使用基于准概率分布的非关节性的连续变量定理，也不能使用离散的可变定理（例如Gottesman-Knill定理）来评估模拟性。我们首先开发一种方法来评估与任意挤压和大量旋转后在位置上测量单个GKP状态相对应的概率密度函数。该方法涉及使用分析数理论的技术评估转换的雅各比theta函数。然后，我们使用此结果来识别两个大型的多模电路，它们在经典上可以有效地模拟，并且不受GKP编码的Clifford组包含。我们的结果扩展了以前已知的电路集，可以在经典上有效地模拟。
We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems such as the Gottesman-Knill theorem can be employed to assess the simulatability. We first develop a method to evaluate the probability density function corresponding to measuring a single GKP state in the position basis following arbitrary squeezing and a large set of rotations. This method involves evaluating a transformed Jacobi theta function using techniques from analytic number theory. We then use this result to identify two large classes of multimode circuits which are classically efficiently simulatable and are not contained by the GKP encoded Clifford group. Our results extend the set of circuits previously known to be classically efficiently simulatable.
