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## 物理代写|热力学代写thermodynamics代考|Implementation in Trapped-Ion Systems

A possible implementation of this approach may involve a string of ions in a linear trap. The qubits, encoded by two internal states of each ion $\left[|g(e)\rangle_j\right]$, are manipulated by laser beams. An additional qubit, encoded by the ground and first excited common vibrational levels $\left(|0(1)\rangle_N\right)$, acts as the “bus mode.” The qubit gates are executed by applying laser pulses on the “carrier” $\left[\Omega_j^{(1)}(t),|g\rangle \leftrightarrow|e\rangle\right]$, the “blue sideband” $\left[\Omega_{j N}^{(2)}(t),|g\rangle|0\rangle \leftrightarrow|e\rangle|1\rangle\right]$, and the “red sideband” $\left[\Omega_{j N}^{(2)^{\top}}(t),|g\rangle|1\rangle \leftrightarrow\right.$ $|e\rangle|0\rangle$ ] of the electronic quadrupole transition [Fig. 13.1(a)]. In a harmonic trap, the blue sideband also couples to higher levels, for example, $|g\rangle|1\rangle \leftrightarrow|e\rangle|2\rangle$, and the red one to $|e\rangle|1\rangle \leftrightarrow|g\rangle|2\rangle$. Such unwarranted excitations complicate and hamper the fidelity of the concurrent application of both two-qubit gates. These excitations may be suppressed by resorting to trap anharmonicity. Dephasing in the trapped-ion system arises due to magnetic-field fluctuations that give rise to random Zeeman shifts of the qubit levels. Simulations of a SWAP gate involving the lowest two common vibrational levels (in an anharmonic trap) in the presence of dephasing [Fig. 13.1(b)] show that the gate fidelity may be raised by means of the optimized pulse sequence compared to its standard counterpart, despite the longer duration of the former.

## 物理代写|热力学代写thermodynamics代考|Decoherence-Free Subspace for Three-Level Multipartite System

In the absence of modulations, decoherence has, in general, no inherent symmetry. Yet, one can dynamically symmetrize the decoherence by appropriate modulations. A “global” dynamical modulation that has the same form, (13.35), for all $N$ particles and levels cannot satisfy $N \gg 1$ symmetrizing requirements at all times. Only different, “local,” modulations applied to the individual particles and levels can cause controlled interference and/or spectral shifts between the couplings of different particles to the bath. The dynamical control matrix elements (13.35) (for $N$ qubits) can then be made to satisfy $2 N$ requirements at all times and be tailored to impose the symmetries described below.

The most desirable symmetry is that of identical coupled particles (ICP), whereby all the modulated particles (and all transitions, in multilevel particles) undergo the same dynamically modified decoherence and cross-decoherence. Then, the following $N \times N$ fully symmetrized decoherence matrix would ensue:
$$J_{j j^{\prime}}^{\mathrm{ICP}}(t)=J(t) \forall j, j^{\prime} .$$
In the case of $N$ qubits that share a single excitation, ICP symmetry would yield to an ( $N-1)$-dimensional decoherence-free subspace (DFS), the entire singleexcitation sector, excluding the totally symmetric entangled state. Any initial state in this DFS would keep perfect fidelity 1 at all times.

Yet, it is generally impossible to impose the ICP symmetry, since it must satisfy too many conditions: $N(N-1) / 2$ conditions for $N$ modulating fields in the case of $N$ qubits [in the case of multilevel particles, there are even more conditions, for each pair of levels $\left.\left(n, n^{\prime}\right)\right]$. Even if we accidently succeeded with $N$ particles, the success would not be scalable to $N+1$ or more particles. Moreover, such symmetry fails completely if not all particles are coupled to all others through the bath, that is, if some $G_{j j^{\prime}}(\omega)$ elements vanish. Nevertheless, in what follows we consider a system of three-level particles where local modulation may impose a DFS.

# 热力学代写

## 物理代写|热力学代写热力学代考|Implementation in trapping -ion Systems

. output – output – output – output – output – output – output

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。