基于迭代李雅普诺夫方法的编码量子门生成
On encoded quantum gate generation by iterative Lyapunov-based methods
AI总结：
本文通过推广参考输入生成算法（RIGA）并构造基于正交投影算子的李雅普诺夫函数，统一解决了闭量子系统中的编码量子门生成、态制备和完全量子门生成问题，并在多个物理案例中验证了算法有效性。
摘要：
本文研究了编码量子门生成问题。其思想是考虑一个维度为 $n$ 的量子系统，该维度高于待合成量子门的维度 $\bar n$。给定 $\mathbb{C}^n$ 的两个正交子集 $\mathbb{E} = \{e_1, e_2, \ldots, e_{\bar n}\}$ 和 $\mathbb F = \{f_1, f_2, \ldots, f_{\bar n}\}$，编码量子门生成问题在于获得一个定义在区间 $[0, T_f]$ 上的开环控制律，使得所有初始态 $e_i$ 都被引导到 $\exp(\jmath ϕ) f_i, i=1,2, \ldots ,\bar n$，并达到某种期望精度和某个全局相位 $ϕ\in \mathbb{R}$。该问题包含了经典的（完全）量子门生成问题（当 $\bar n = n$ 时）、态制备问题（当 $\bar n = 1$ 时），以及编码门生成问题（当 $1 < \bar n < n$ 时）。因此，这里将三个问题统一在一个共同的框架中。本文推广了参考输入生成算法（Reference Input Generation Algorithm，RIGA），用于考虑闭量子系统的编码门生成问题。从编码门支撑集上的正交投影算子导出了一个合适的李雅普诺夫函数。三个具有物理意义的案例研究表明了该数值算法的潜在价值：两个耦合的 transmon 量子比特、一个与 transmon 量子比特耦合的腔模，以及一条包含 $N$ 个量子比特的链，其中包括 $N=10$ 的大维度情形。
英文摘要：
The problem of encoded quantum gate generation is studied in this paper. The idea is to consider a quantum system of higher dimension $n$ than the dimension $\bar n$ of the quantum gate to be synthesized. Given two orthonormal subsets $\mathbb{E} = \{e_1, e_2, \ldots, e_{\bar n}\}$ and $\mathbb F = \{f_1, f_2, \ldots, f_{\bar n}\}$ of $\mathbb{C}^n$, the problem of encoded quantum gate generation consists in obtaining an open loop control law defined in an interval $[0, T_f]$ in a way that all initial states $e_i$ are steered to $\exp(\jmath ϕ) f_i, i=1,2, \ldots ,\bar n$ up to some desired precision and to some global phase $ϕ\in \mathbb{R}$. This problem includes the classical (full) quantum gate generation problem, when $\bar n = n$, the state preparation problem, when $\bar n = 1$, and finally the encoded gate generation when $ 1 < \bar n < n$. Hence, three problems are unified here within a unique common approach. The \emph{Reference Input Generation Algorithm (RIGA)} is generalized in this work for considering the encoded gate generation problem for closed quantum systems. A suitable Lyapunov function is derived from the orthogonal projector on the support of the encoded gate. Three case-studies of physical interest indicate the potential interest of such numerical algorithm: two coupled transmon-qubits, a cavity mode coupled to a transmon-qubit, and a chain of $N$ qubits, including a large dimensional case for which $N=10$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
