任意纯高斯态下三次相位门的精确Fock振幅
Exact Fock Amplitudes of the Cubic-Phase Gate on Arbitrary Pure Gaussian States
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中文总结 AI 辅助
本文针对任意纯单模高斯输入，推导了三次相位门Fock振幅的闭式解，以Airy函数组合表示，并给出递推关系及截断误差分析。
中文摘要 AI 辅助
三次相位门是通用连续变量量子计算中唯一的非高斯元件。其Fock振幅仅在输入为Fock态时才具有闭式解。对于高斯输入，通常的方法是在截断的Fock空间中构造三次正交算符并对其求指数，这会在取指数之前改变生成元。本文针对任意纯单模高斯输入（包括沿任意正交轴的压缩、任意位移和升压）获得了闭式解。该解是Airy函数及其导数的有限组合，且其参数对所有Fock指标共享，因此整个Fock分布只需两次Airy函数求值。本文还推导了一个递推关系，可由前四个系数构建每个系数，并给出了该递推关系稳定的参数范围。在评估当前实验的弱非线性下的闭式解时需谨慎，因为其各项会增大并交替变号。本文量化了所需的精度，并将截断构造与精确结果进行了基准比较，发现在常用截断下的误差与所计算量本身的大小相当。
英文摘要
The cubic phase gate is the only non-Gaussian element of universal continuous-variable quantum computation. Its Fock amplitudes are known in closed form only when the input is a Fock state. For a Gaussian input the usual route is to build the cubic quadrature in a truncated Fock space and exponentiate it, which alters the generator before the exponential is taken. A closed form is obtained here for every pure single-mode Gaussian input, with the squeezing along any quadrature axis and with arbitrary displacement and boost. It is a finite combination of the Airy function and its derivative, and the argument is shared by all Fock indices, so a whole Fock profile costs two Airy evaluations. A recurrence is also derived that builds each coefficient from the four preceding ones, together with the regime in which it is stable. Evaluating the closed form at the weak nonlinearities of current experiments requires care, since its terms grow large and alternate in sign. The precision this demands is quantified, and the truncated construction is benchmarked against the exact result, whose error at cutoffs in common use is found to be of the same size as the quantity being computed.
发表机构
- Islamic Azad University（伊斯兰阿扎德大学）
机构由 AI 辅助整理，请以论文原文为准。
