## 物理代写|量子计算代写Quantum computer代考|PHYS14

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Basic Operations with Qubits

Consider basic operations with qubits.
A quantum gate effect on qubit $|\psi\rangle$ occurs by applying the quantum-mechanical operator, e.g. $U|\psi\rangle[1-3]$. Operators can be represented as unitary matrices. In particular, the evolution of a single qubit is described by a unitary matrix of size $2 \times 2$

The consistent application of a number of operators $U_{1}, U_{2}, \ldots, U_{n}$ to one qubit is equivalent to the effect of some operator $W$ in the form
$$W|\psi\rangle=U_{n}\left(U_{n-1}\left(\ldots\left(U_{2}\left(U_{1}|\psi\rangle\right)\right) \ldots\right)\right)=\left(U_{1} U_{2} \ldots U_{n}\right)|\psi\rangle$$
Its matrix $M_{W}$ is a product of matrices of $U_{i}, i=1,2, \ldots, n$, in the reverse order [4]:
$$M_{W}=M_{U_{n}} M_{U_{n-1}} \ldots M_{U_{1}} .$$
Such an operator $W$ is called a product of operators $U_{1}, U_{2}, \ldots, U_{n}$. Due to the noncommutativity of the matrix multiplication operation, the order in which quantum gates are applied is generally important.

Example 3.1 Let us show that the application of the operator $\sigma_{3}$ (see definition (2.1)) to a qubit in the state $|\psi\rangle=u|0\rangle+v|1\rangle$ brings it to the state $\left|\psi^{\prime}\right\rangle=u|0\rangle-v|1\rangle$.
Proof.
Write a qubit $|\psi\rangle$ in matrix notation:
$$|\psi\rangle=\left[\begin{array}{l} u \ v \end{array}\right] \text {. }$$
Let us define the action of $\sigma_{3}$ on this quantum state:
$$\left|\psi^{\prime}\right\rangle=\sigma_{3}\left[\begin{array}{l} u \ v \end{array}\right]=\left[\begin{array}{cc} 1 & 0 \ 0 & -1 \end{array}\right]\left[\begin{array}{l} u \ v \end{array}\right]=\left[\begin{array}{c} u \ -v \end{array}\right]=u\left[\begin{array}{l} 1 \ 0 \end{array}\right]-v\left[\begin{array}{l} 0 \ 1 \end{array}\right]=u|0\rangle-v|1\rangle \text {. }$$

## 物理代写|量子计算代写Quantum computer代考|The graphic representation of quantum operations

The graphic representation of quantum operations in the form of circuits or diagrams (quantum circuits) is widely used.

A quantum circuit, or network, is an ordered sequence of elements and communication lines connecting them, i.e. wires. Usually, only acyclic circuits are considered in which data flow in one direction-from left to right, and the wires do not return bits to the previous position in the circuit. Input states are attributed to the wires coming from the left. In one time step, each wire may enter data in no more than one gate. The output states are read from the communication lines coming out of the circuit on the right.

As you can see, the circuit solves a problem of a fixed size. Unlike the quantum circuit, quantum algorithms are defined for input data of any size [5].

A quantum-mechanical operator $U$, which converts a one-qubit gate, is presented as follows:
$$\left|\psi_{\text {in }}\right\rangle-U$$
The sequence of the quantum algorithm steps corresponds to the direction on the circuit from left to right.

Table $3.1$ lists the frequently used gates that convert one qubit and the matrix notations of these gates.

Let us show the computation method of the quantum operation matrix based on its effect on basis vectors.
The Hadamard ${ }^{1}$ gate converts the system state in accordance with the rule:
\begin{aligned} &|0\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle), \ &|1\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle) . \end{aligned}
Consequently, the arbitrary state $|\psi\rangle$ will change in this case as follows:
\begin{aligned} |\psi\rangle &=\left[\begin{array}{c} u \ v \end{array}\right]=u\left[\begin{array}{l} 1 \ 0 \end{array}\right]+v\left[\begin{array}{l} 0 \ 1 \end{array}\right] \ & \rightarrow u \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)+v \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)=\frac{1}{\sqrt{2}}\left[\begin{array}{cc} 1 & 1 \ 1 & -1 \end{array}\right]\left[\begin{array}{l} u \ v \end{array}\right] \end{aligned}
Thus, the Hadamard gate, or the Hadamard element, corresponds to the matrix $\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1 & 1 \ 1 & -1\end{array}\right]$.

Of course, to execute complex algorithms, the qubits must interact with each other and exchange information. In this regard, logical operations involving two or more qubits are of special importance. In Table $3.2$ are listed the most important gates that transform the state of two qubits.

## 物理代写|量子计算代写Quantum computer代考|The following quantum state is set

$$|\psi\rangle=\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}} e^{\mathrm{i} \varphi}|1\rangle,$$
where $\varphi$ is a real number. Let us define the result of measuring this state in bases $B_{1}=$ ${|0\rangle,|1\rangle}$ and $B_{2}={|+\rangle,|-\rangle}$, where $|+\rangle=\frac{1}{2}(|0\rangle+|1\rangle)$ and $|-\rangle=\frac{1}{2}(|0\rangle-|1\rangle)$.
Solution.
First of all, we consider the basis $B_{1}$. According to the measurement postulate (see Appendix A on page 105), the probabilities of getting 0 or 1 as a result of the measurement of the state $u|0\rangle+v|1\rangle$ is equal to $|u|^{2}$ and $|v|^{2}$, respectively. In our example, $u=\frac{1}{\sqrt{2}}$ and $v=\frac{1}{\sqrt{2}} e^{i \varphi}$, therefore the result of the measurement of $M$ is
$$M=\left{\begin{array}{l} 0 \text { with a probability of } p_{0}=\frac{1}{2}, \ 1 \text { with a probability of } p_{1}=\frac{1}{2} \end{array}\right.$$
Note that information about the value of $\varphi$ using a measurement in the basis $B_{1}$ cannot be obtained.

Let us turn to measurement using the second basis $B_{2}={|+\rangle,|-\rangle}$. We express the vectors of the computational basis through $|+\rangle$ and $|-\rangle}$ :
\begin{aligned} |0\rangle &=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle), \ |1\rangle &=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle) . \end{aligned}
In this regard, we obtain
\begin{aligned} |\psi\rangle &=\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}} e^{\mathrm{i} \varphi}|1\rangle \ &=\frac{1}{2}(|+\rangle+|-\rangle)+\frac{1}{2} e^{\mathrm{i} \varphi}(|+\rangle+|-\rangle) \ &=\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right)|+\rangle+\frac{1}{2}\left(1-e^{\mathrm{i} \varphi}\right)|-\rangle . \end{aligned}
The probability of finding the system in the state $|+\rangle$ is
\begin{aligned} p_{+} &=\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right) \times\left(\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right)\right)^{*} \ &=\frac{1}{4}\left(1+e^{\mathrm{i} \varphi}\right)\left(1+e^{-\mathrm{i} \varphi}\right)=\frac{1}{4}\left(2+e^{\mathrm{i} \varphi}+e^{-\mathrm{i} \varphi}\right) \end{aligned}

## 物理代写|量子计算代写Quantum computer代考|Basic Operations with Qubits

$$W|\psi\rangle=U_{n}\left(U_{n-1}\left(\ldots\left(U_{2}\left(U_{1}|\psi\rangle\right)\right) \ldots\right)\right)=\left(U_{1} U_{2} \ldots U_{n}\right)|\psi\rangle$$

$$M_{W}=M_{U_{n}} M_{U_{n-1}} \ldots M_{U_{1}} .$$

$$|\psi\rangle=[u v] .$$

$$\left|\psi^{\prime}\right\rangle=\sigma_{3}\left[\begin{array}{ll} u & v \end{array}\right]=\left[\begin{array}{llll} 1 & 0 & 0 & -1 \end{array}\right]\left[\begin{array}{ll} u & v \end{array}\right]=\left[\begin{array}{ll} u-v \end{array}\right]=u\left[\begin{array}{ll} 1 & 0 \end{array}\right]-v\left[\begin{array}{ll} 0 & 1 \end{array}\right]=u|0\rangle-v|1\rangle .$$

## 物理代写|量子计算代写Quantum computer代考|The graphic representation of quantum operations

$$\left|\psi_{\text {in }}\right\rangle-U$$

$$|0\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle), \quad|1\rangle \rightarrow \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle) .$$

$$|\psi\rangle=[u v]=u\left[\begin{array}{ll} 1 & 0 \end{array}\right]+v\left[\begin{array}{ll} 0 & 1 \end{array}\right] \quad \rightarrow u \frac{1}{\sqrt{2}}(|0\rangle+|1\rangle)+v \frac{1}{\sqrt{2}}(|0\rangle-|1\rangle)=\frac{1}{\sqrt{2}}\left[\begin{array}{llll} 1 & 1 & -1 \end{array}\right][u v]$$

## 物理代写|量子计算代写Quantum computer代考|The following quantum state is set

$$|\psi\rangle=\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}} e^{\mathrm{i} \varphi}|1\rangle$$

$$|0\rangle=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle),|1\rangle \quad=\frac{1}{\sqrt{2}}(|+\rangle+|-\rangle) .$$

$$|\psi\rangle=\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}} e^{\mathrm{i} \varphi}|1\rangle \quad=\frac{1}{2}(|+\rangle+|-\rangle)+\frac{1}{2} e^{\mathrm{i} \varphi}(|+\rangle+|-\rangle)=\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right)|+\rangle+\frac{1}{2}\left(1-e^{\mathrm{i} \varphi}\right)$$

$$p_{+}=\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right) \times\left(\frac{1}{2}\left(1+e^{\mathrm{i} \varphi}\right)\right)^{*}=\frac{1}{4}\left(1+e^{\mathrm{i} \varphi}\right)\left(1+e^{-\mathrm{i} \varphi}\right)=\frac{1}{4}\left(2+e^{\mathrm{i} \varphi}+e^{-\mathrm{i} \varphi}\right)$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|CS583

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Pauli Matrices and Dirac Matrices

For the imaginary unit $\sqrt{-1}$, we will use the designation $i \equiv \sqrt{-1}$. The matrices $\sigma_{1}, \sigma_{2}$, and $\sigma_{3}$ :
$$\sigma_{1}=\left[\begin{array}{ll} 0 & 1 \ 1 & 0 \end{array}\right], \quad \sigma_{2}=\left[\begin{array}{cc} 0 & -\mathrm{i} \ \mathrm{i} & 0 \end{array}\right], \quad \sigma_{3}=\left[\begin{array}{cc} 1 & 0 \ 0 & -1 \end{array}\right],$$
are called the Pauli matrices. They are widely used in quantum theory for describing half-integer spin particles, for example, an electron. (Spin is a quantum property of an elementary particle, its intrinsic angular momentum [1]. So, electrons, protons, and neutrinos have half-integer spin; the spin of photons and gravitons is an integer.).
The following properties are valid for the Pauli matrices.
(1) The Pauli matrices are Hermitian ${ }^{1}$ and unitary (see Appendix B on page 103):
$$\forall k \in{1,2,3} \quad \sigma_{k}=\sigma_{k}^{\dagger}=\sigma_{k}^{-1} .$$
(2) $\forall k \in{1,2,3}$, the square of the Pauli matrix is equal to the identity matrix:
$$\sigma_{i}^{2}=\left[\begin{array}{ll} 1 & 0 \ 0 & 1 \end{array}\right]$$
(3) $\forall i, j \in{1,2,3}$, the equalities
$$\sigma_{i} \sigma_{j}+\sigma_{j} \sigma_{i}=2 \delta_{i j}\left[\begin{array}{ll} 1 & 0 \ 0 & 1 \end{array}\right]$$
are valid. Here, is used a notation for the Kronecker symbol (see definition on page 3 ).
Note that the value ${A, B}=A B+B A$ is usually called anticommutator of matrices $A$ and $B$, and the value $[A, B]=A B-B A$ is called commutator. Next,for the identity matrix, we will apply the notation $I$, and for the zero one $O$. In particular, the formula (2.4) can be written as follows:
$$\left{\sigma_{i}, \sigma_{j}\right}=2 \delta_{i j} I .$$
The matrices $A$ and $B$ are called commutative, if $A B=B A$. Commutative matrices are always square and have the same order.

By definition, the condition $[A, B]=O$ is met for the commutative matrices [2]. It is clear that the Pauli matrices do not commutate with each other (see Exercise 1).

## 物理代写|量子计算代写Quantum computer代考|Let us prove the Jacobi2 identity

$$[[P, Q], R]+[[Q, R], P]+[[R, P], Q] \equiv O$$
that is valid for commutators of any matrices of size $n \times n$.
Proof.
We use the definition of the commutator $[P, Q]=P Q-Q P$, then
\begin{aligned} {[[P, Q], R] } &=[P Q-Q P, R]=(P Q-Q P) R-R(P Q-Q P) \ &=P Q R-Q P R-R P Q+R Q P \end{aligned}
Next, let us present in a similar manner the remaining summands in the sum:
\begin{aligned} &{[[Q, R], P]=Q R P-R Q P-P Q R+P R Q} \ &{[[R, P], Q]=R P Q-P R Q-Q R P+Q P R .} \end{aligned}
The sum of right-hand values (2.7), (2.8), and (2.9), as can be easily seen after the conversion of such summands, is zero. In this way, the Jacobi identity is proved.
Sometimes, in linear algebra and its applications, one has to use matrices split into rectangular parts or blocks [3,4]. Consider the rectangular matrix $A=\left(a_{i j}\right)$, where $1 \leqslant i \leqslant m, 1 \leqslant j \leqslant n$. Let $m=m_{1}+m_{2}$ and $n=n_{1}+n_{2}$.

Let us draw horizontal and vertical lines and split the matrix $A$ into four rectangular blocks:Thus, the matrix $A$ is presented in the form of a block matrix, consisting of the blocks $B_{11}, B_{12}, B_{21}$, and $B_{22}$ of size $m_{1} \times n_{1}, m_{1} \times n_{2}, m_{2} \times n_{1}$, and $m_{2} \times n_{2}$, respectively.

## 物理代写|量子计算代写Quantum computer代考|Dirac matrices

As an example of a block matrix setting, we provide the definition of the Dirac matrices. Four Dirac matrices $\alpha_{1}, \alpha_{2}, \alpha_{3}$, and $\beta$ are part of the equation named after him for a half-integer spin relativistic particle, and are expressed in terms of the Pauli matrices $\sigma_{k}, k=1,2,3$, as follows [5]:
$$\alpha_{k}=\left[\begin{array}{cc} O & \sigma_{k} \ \sigma_{k} & O \end{array}\right], \quad \beta=\left[\begin{array}{cc} I & O \ O & -I \end{array}\right]$$
(Relativistic particles are the particles whose velocity is close to the velocity of light.)
Each of the Dirac matrices has a Hermitian property and a property of being unitary. Moreover, for all $l, m \in{1,2,3}$ the equalities
\begin{aligned} \alpha_{l} \alpha_{m}+\alpha_{m} \alpha_{l} &=2 \delta_{l m} I, \ \alpha_{l} \beta+\beta \alpha_{l} &=O \end{aligned}
are valid. Note that the size of matrices $I$ and $O$ in formulas (2.12) and (2.13) is equal to $4 \times 4$.

Using the concept of a block matrix, it is easy to write down the definition of the tensor product of square matrices $A \otimes B$, defined as $A=\left(a_{i j}\right), i, j=1,2, \ldots, n_{A}$, and $B=\left(b_{i j}\right), i, j=1,2, \ldots, n_{B}$ :
$$A \otimes B=\left[\begin{array}{cccc} a_{11} B & a_{12} B & \ldots & a_{1 n_{A}} B \ a_{21} B & a_{22} B & \ldots & a_{2 n_{A}} B \ \vdots & \vdots & \ddots & \vdots \ a_{n_{A} 1} B & a_{n_{A} 2} B & \ldots & a_{n_{A} n_{A}} B \end{array}\right]$$
where $a_{11} B$ is a block with size $n_{B} \times n_{B}$, consisting of elements of the form $a_{11} b_{i j}$, block $a_{12} B$ consists of elements of the form $a_{12} b_{i j}$, etc.

Note that for the tensor product operation, the sizes of matrices $A$ and $B$ do not have to be the same, i.e. $n_{A} \neq n_{B}$.

## 物理代写|量子计算代写Quantum computer代考|Pauli Matrices and Dirac Matrices

σ1=[01 10],σ2=[0−一世 一世0],σ3=[10 0−1],

(1) Pauli 矩阵是 Hermitian 矩阵1和单一的（参见第 103 页的附录 B）：

∀ķ∈1,2,3σķ=σķ†=σķ−1.
(2) ∀ķ∈1,2,3，泡利矩阵的平方等于单位矩阵：

σ一世2=[10 01]
(3) ∀一世,j∈1,2,3, 等式

σ一世σj+σjσ一世=2d一世j[10 01]

\left{\sigma_{i}, \sigma_{j}\right}=2 \delta_{i j} I 。\left{\sigma_{i}, \sigma_{j}\right}=2 \delta_{i j} I 。

## 物理代写|量子计算代写Quantum computer代考|Let us prove the Jacobi2 identity

$$[[P, Q], R]+[[Q, R], P]+[[R, P], Q] \equiv O$$

$$[[P, Q], R]=[P Q-Q P, R]=(P Q-Q P) R-R(P Q-Q P) \quad=P Q R-Q P R-R P Q+R Q P$$

$$[[Q, R], P]=Q R P-R Q P-P Q R+P R Q \quad[[R, P], Q]=R P Q-P R Q-Q R P+Q P R$$

## 物理代写|量子计算代写Quantum computer代考|Dirac matrices

(相对论粒子是速度接近光速的粒子。)

$$\alpha_{l} \alpha_{m}+\alpha_{m} \alpha_{l}=2 \delta_{l m} I, \alpha_{l} \beta+\beta \alpha_{l} \quad=O$$

$A \otimes B=\left[\begin{array}{lllllllllll}a_{11} B & a_{12} B & \ldots & a_{1 n_{A}} B & a_{21} B & a_{22} B & \ldots & a_{2 n_{A}} B & \vdots & \ddots & \vdots a_{n_{A} 1} B\end{array}\right.$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Physics 421

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Quantum Computing Model

Quantum computers use processes of a quantum nature manifested with atoms, molecules, molecular clusters, etc. The description of such processes is based on the application of complex numbers and complex matrices.

As is well known, the basic notion of classical information theory is a bit [1]. A classical bit takes the values 0 or 1 (and no other).

A qubit (quantum bit) is the smallest element that executes the information storage function in a quantum computer [2].

Qubit is a quantum system $|\psi\rangle$ that allows two states: $|0\rangle$ and $|1\rangle$. In accordance with the so-called “bra-ket” Dirac ” notation (from word bra(c)ket), the symbols $\mid 0$ ) and $|1\rangle$ are read as “Ket $0 “$ and “Ket 1 “, respectively. The brackets $|. .\rangle\rangle$ show that $\psi$ is some state of the quantum system.

The fundamental difference between the classical bit and the qubit consists in that, the qubit can be in a state different from $|0\rangle$ or $|1\rangle$. The arbitrary state of the qubit is defined by the linear combination of basis states:
$$|\psi\rangle=u|0\rangle+v|1\rangle,$$
where the complex coefficients $u$ and $v$ satisfy the following normalization condition:
$$|u|^{2}+|v|^{2}=1 .$$
The mathematical description of basis states reduces to their representation in matrix form:
$$|0\rangle=\left[\begin{array}{l} 1 \ 0 \end{array}\right], \quad|1\rangle=\left[\begin{array}{l} 0 \ 1 \end{array}\right]$$
Based on the presentation (1.3), the arbitrary state of the qubit is written as
$$|\psi\rangle=\left[\begin{array}{l} u \ v \end{array}\right]$$

## 物理代写|量子计算代写Quantum computer代考|The orthogonality condition

The orthogonality condition of two states $\left|\psi^{\prime}\right\rangle$ and $\left|\psi^{\prime \prime}\right\rangle$ is written as follows:
$$\left\langle\psi^{\prime} \mid \psi^{\prime \prime}\right\rangle=\sum_{i=1}^{2^{n}} u_{i}^{*} v_{i}=0 .$$
Note that the states of the computational base (1.6) are orthonormalized.
To change the state of a quantum system, quantum operations are used, which are called quantum logic gates, or, for short, simply gates. Thus, gates perform logical operations on qubits. Note that the change of state $|\psi\rangle$ in time is also referred to as the evolution of the quantum system.

An important step of quantum algorithms is the procedure of measurement of a state. When the qubit state is measured, it randomly passes to one of its states: $|0\rangle$ or $|1\rangle$. Therefore, the complex coefficients $u$ and $v$ from the qubit definition (1.1) are associated with the probability to get the value 0 or 1 when its state is measured. According to the postulates of quantum theory, the probabilities of passing to the states $|0\rangle$ and $|1\rangle$ are equal to $|u|^{2}$ and $|v|^{2}$, respectively. In this connection, the equality (1.2) reflects the probability conservation law. After the measurement, the qubit passes to the basis state, complying with the classical result of the measurement. Generally speaking, the probabilities of getting the result 0 and 1 are different for different states of the quantum system.

In other words, quantum computing is a sequence of simple form operations with the collection of the interacting qubits. In the final step of the quantum computing procedure, the state of the quantum system is measured and a conclusion about the computing result is made. The measurement makes it possible to obtain, at a macroscopic level, the information about the quantum state. The peculiarity of the quantum measurements is their irreversibility, which radically differentiates quantum computing from the classical one.

Despite the fact that the number of qubit states is infinite, with the help of measurement it is possible to obtain only one bit of classical information. The measurement procedure transfers the qubit state to one of the basis states, so a second measurement will produce the same result.

Quantum computer is a set of $n$ qubits controlled by external (classic) signals [812]. Often, an ordered set of some qubits is called a register. The main elements of a quantum computer are shown in Fig. 1.1.

The classical quantum computer setting consists of the controlling classical computer and impulse generators controlling the qubit evolution, as well as measurement instruments of the qubit state. The system from $n$ qubits in the initial state, e.g. $\left|\psi_{\text {in }}\right\rangle=|00 \ldots 0\rangle$, forms a memory register prepared to record input data and perform computations. The data are recorded by an external action on each of the system’s qubits. The solution of the problem is determined by a measurement of the final state qubits $\left|\psi_{\text {out }}\right\rangle[2,12]$.

## 物理代写|量子计算代写Quantum computer代考|Main elements of a quantum computer

In this record, the state $|\psi\rangle$ of the $n$-qubit register of a quantum computer is expressed through the superposition of vectors of computational basis $B={|0\rangle,|1\rangle, \ldots$, $\left.\left|2^{n}-1\right\rangle\right}$ by the formula
$$|\psi\rangle=\sum_{k=0}^{2^{n}-1} c_{k}|k\rangle$$
where the normalization condition
$$\sum_{k=0}^{2^{k}-1}\left|c_{k}\right|^{2}=1$$
is met.
A quantum system, formed by $N$ two-level elements, has $\Sigma(N)=2^{N}$ independent states. The key point of the functioning of such a system is the interaction of separate qubits with each other. The number of states $\Sigma(N)$ grows exponentially with the growth of the quantum system, which allows solving practical problems of a very high asymptotic complexity. For example, an efficient quantum algorithm of prime factorization is known, which is very important for cryptography [13]. As a result, the quantum algorithms provide exponential or polynomial speedup in comparison with the classical solution methods for many problems.

Unfortunately, no full-function quantum computer has been created yet, although many of its elements have already been built and studied at the world’s leading laboratories $[11,14,15]$. The main obstacle to the development of quantum computing is the instability of a system of many qubits. The more the qubits are united into an entangled system, the more the effort is required to ensure the smallness of the number of measurement errors. Nevertheless, the history of quantum computer development demonstrates an enormous potential laid in the uniting of quantum theory and algorithm theory.

## 物理代写|量子计算代写Quantum computer代考|Quantum Computing Model

qubit（量子位）是量子计算机中执行信息存储功能的最小元素[2]。

Qubit是一个量子系统|ψ⟩允许两种状态：|0⟩和|1⟩. 根据所谓的“bra-ket”狄拉克“符号（来自单词 bra(c)ket），符号∣0） 和|1⟩读作“凯0“和“Ket 1”，分别。括号|..⟩⟩显示ψ是量子系统的某种状态。

|ψ⟩=在|0⟩+在|1⟩,

|在|2+|在|2=1.

|0⟩=[1 0],|1⟩=[0 1]

|ψ⟩=[在 在]

## 物理代写|量子计算代写Quantum computer代考|The orthogonality condition

⟨ψ′∣ψ′′⟩=∑一世=12n在一世∗在一世=0.

## 物理代写|量子计算代写Quantum computer代考|Main elements of a quantum computer

|ψ⟩=∑ķ=02n−1Cķ|ķ⟩

∑ķ=02ķ−1|Cķ|2=1

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Understanding the Qiskit® Gate Library

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Visualizing quantum gates

To help us understand quantum gates, we can use the ch6_rl_quantum_gate_ui .py sample program.
This recipe differs a bit from the ones that we have seen so far. Up until now, we have mainly just used Qiskit” commands inside a Python wrapper, with no actual coding beyond that. This time, we start out by building a rudimentary Python implementation to create a very basic before-after gate exploration UI. When you run the program, it prompts you to select an initial qubit state and a gate to apply to your qubit; then it creates a visualization to show you the gate action on the qubit.
The script builds your circuit for you and then shows the basic minimum circuit that supports the gate, the state vector, and a Bloch sphere or Q-sphere visualization that corresponds to the gate action. The visualization highlights the qubit’s state before the gate, and how the state changes after the gate.

Before we step into the visualizer, let’s spend a second discussing a few basic qubit states that we can initialize our qubit in. You know two of them $(|0\rangle$ and $|1\rangle)$ well, but for an understanding of where on the Bloch sphere our qubit state vector points, here’s a quick introduction of the rest with their Dirac ket description and a Bloch sphere reference:

• $|0\rangle=|0\rangle$ : Straight up along the $z$ axis
• $|1\rangle=|1\rangle$ : Straight down along the $z$ axis
• $1+\rangle=\frac{|0\rangle+|1\rangle}{\sqrt{2}}$ : Out along the $+x$ axis
• $|-\rangle=\frac{|0\rangle-|1\rangle}{\sqrt{2}}$ : In along the $-x$ axis
• $|\mathrm{R}\rangle=\frac{|0\rangle+1|1\rangle\rangle}{\sqrt{2}}$ : Right along the $+y$ axis
• $|\mathbf{L}\rangle=\frac{|0\rangle-i|1\rangle}{\sqrt{2}}$ : Left along the $-y$ axis

## 物理代写|量子计算代写Quantum computer代考|Flipping with the Pauli X, Y, and Z gates

The Pauli X, $\mathrm{Y}$, and $\mathrm{Z}$ gates all act on a single qubit, and perform an action similar to a classical NOT gate, which flips the value of a classical bit. For example, the $\mathrm{X}$ gate sends $|0\rangle$ to $|1\rangle$ and vice versa.

As we shall see, the $\mathrm{X}$ gate is actually a rotation around the $x$ axis of $\pi$ radians. The same is true for the Pauli $Y$ and $Z$ gates, but along the $y$ and $z$ axes correspondingly.

Mathematically, the X, Y, and $Z$ gates can be expressed as the following unitary matrixes:
$$X=\left[\begin{array}{ll} 0 & 1 \ 1 & 0 \end{array}\right] Y=\left[\begin{array}{cc} 0 & -i \ i & 0 \end{array}\right] Z=\left[\begin{array}{cc} 1 & 0 \ 0 & -1 \end{array}\right]$$
This recipe will serve as a sort of template for how to use the sample code that is provided in the chapter. The remaining recipes will largely gloss over the deeper details.

Let’s take a look at the Pauli X, Y, and Z gates by running the Quantum Gate UI sample program. It starts by setting up a plain quantum circuit with a single qubit initiated in a state that you select. The gate selected is then added to the circuit, and then the unitary simulator and state vector simulators are run to display the results in the form of a qubit state vector and the gate unitary matrix.
The sample script is available at: https://github . com/ Packt Publishing/ Quantum-Computing-in-Practice-with-Qiskit-and-IBM-QuantumExperience/blob/master/Chapter06/ch6_r1_quantum_qate_ui.py.

## 物理代写|量子计算代写Quantum computer代考|Creating superpositions with the H gate

Now, let’s revisit our old friend from Chapter 4, Starting at the Ground Level with Terra, the Hadamard or $\mathbf{H}$ gate. This is a fairly specialized gate that we can use to make a generic qubit superposition. But there’s more to it than that; we can also make use of the $\mathrm{H}$ gate to change the axis of measurement from the generic $z$ (or computational) axis to the $x$ axis to gain additional insights into the qubit behavior. More on that in the There’s more section.
The $\mathrm{H}$ gate can be expressed as the following unitary matrix:
$$H=\frac{1}{\sqrt{2}}\left[\begin{array}{cc} 1 & 1 \ 1 & -1 \end{array}\right]$$
Unless you are really good at interpreting matrix operations, it might not be entirely clear just what this gate will do with your qubits. If we describe the behavior as a combination of 2 qubit rotations instead, things might become clearer. When you apply the Hadamard gate to your qubit, you run it through two rotations: first a $\frac{\pi}{2}$ rotation around the $y$ axis, and then a $\pi$ rotation around the $x$ axis.

For a qubit in state $|0\rangle$, this means that we start at the North Pole, and then travel down to the equator, ending up at the $|+\rangle$ location on the Bloch sphere, and finally just rotate around the $x$ axis. Similarly, if you start at the South Pole at $|1\rangle$, you first move up to the equator but at the other extreme on the $x$ axis, ending up at $|-\rangle$.
If we do the matrix math for $|0\rangle$, we get the following:
$$\frac{1}{\sqrt{2}}\left[\begin{array}{cc} 1 & 1 \ 1 & -1 \end{array}\right]\left[\begin{array}{l} 1 \ 0 \end{array}\right]=\frac{1}{\sqrt{2}}\left[\begin{array}{l} 1 \ 1 \end{array}\right]$$

Now we can use the following Dirac ket notation:
$$|\psi\rangle=a|0\rangle+b|1\rangle$$
where, $\mathrm{a}=\cos \left(\frac{\theta}{2}\right), \mathrm{b}=\mathrm{e}^{\mathrm{i} \varphi} \sin \left(\frac{\theta}{2}\right)$
If we replace $a$ and $b$ with $1 / \sqrt{2}$ from above, we get: $\theta=\pi / 2$ and $\varphi=0$, which corresponds to $|+\rangle$
If we apply the Hadamard gate to qubits in states other than pure $|0\rangle$ and $|1\rangle$, we rotate the qubit to a new position.
The sample script is available at: https://github. com/Packt Publishing/ Quantum-Computing-in-Practice-with-Qiskit-and-IBM-QuantumExperience/blob/master/Chapter $06 / \mathrm{ch} 6$ _l_quantum_qate_ui.py.

## 物理代写|量子计算代写Quantum computer代考|Visualizing quantum gates

• |0⟩=|0⟩: 沿着直线上升和轴
• |1⟩=|1⟩: 沿着直线向下和轴
• 1+⟩=|0⟩+|1⟩2: 沿着+X轴
• |−⟩=|0⟩−|1⟩2: 在沿着−X轴
• |R⟩=|0⟩+1|1⟩⟩2: 就在+是轴
• |大号⟩=|0⟩−一世|1⟩2: 沿着左边−是轴

## 物理代写|量子计算代写Quantum computer代考|Flipping with the Pauli X, Y, and Z gates

X=[01 10]是=[0−一世 一世0]从=[10 0−1]

## 物理代写|量子计算代写Quantum computer代考|Creating superpositions with the H gate

H=12[11 1−1]

12[11 1−1][1 0]=12[1 1]

|ψ⟩=一个|0⟩+b|1⟩

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Touring the IBM Quantum® Hardware with Qiskit®

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|What are the IBM Quantum® machines

This section is less of a recipe and rather more of a basic overview of the quantum components and processes that you will be encountering. If you’d rather jump ahead and start coding right away, then go to the next recipe.

With Qiskit”, you can run your quantum programs on two types of quantum computers: simulators and IBM Quantum” hardware. The simulators run either locally or in the cloud on IBM hardware. Generally speaking, running a simulator in the cloud gives you greater power and performance; ibmq_gasm_simulator – available online – lets you run fairly deep quantum programs on up to 32 qubits. Your local simulator performance depends on your hardware; remember that simulating a quantum computer gets exponentially harder with each qubit added.The actual IBM quantum computer hardware is located in an IBM lab and is accessed through the cloud. There are good reasons for this, so let’s walk through this recipe on how to set up and run a quantum computer with the superconducting qubits that IBM Quantum ${ }^{*}$ provides.

Superconducting quantum computers are extremely sensitive to noise such as electromagnetic radiation, sound waves, and heat. An isolated environment equipped with cryogenic cooling provides a location with as little disturbance as possible.
Quantum computers may use so-called Josephson junctions kept at cryogenic temperatures and manipulated by microwave pulses. Ordinary people do not possess this kind of hardware, so, in this book, we will use the freely available IBM quantum computers in the cloud for our quantum programming.

## 物理代写|量子计算代写Quantum computer代考|Locating the available backends

In Qiskit”, a backend represents the system on which you run your quantum program. A backend can be a simulator, like the local Aer simulator that we have used earlier. If you want to run your quantum programs on real quantum computers instead of on your local simulator, you must identify an IBM Quantum” machine as a backend to use, and then configure your quantum program to use it.
Let’s see the steps of what we’ll be doing:

1. Start by importing the required classes and methods and load your account information. In this case, we use the IBMQ class, which contains the main hardware-related functions.
2. Take a look at the machines that are available to your account.
3. Select a generally available backend.
4. Create and run a Bell state quantum program on the selected backend.
5. Select a simulator backend and run the Bell state quantum program again for comparison.
In this recipe, we will use the IBMQ provider .backends () method to identify and filter available backends to run your programs and then use the provider.get backend () method to select the backend. In the example that follows, we will use the ibmqx2 and ibmq_qasm_simulator backends. We will then run a small quantum program on one of the hardware backends, and then on the simulator backend.
The Python file in the following recipe can be downloaded from here: https : // github. com/PacktPublishing/Quantum-Computing-in-Practice-withQiskit-and-IBM-Quantum-Experience/blob/master/Chapter05/ch5_ r1_identifying_backends.py .

## 物理代写|量子计算代写Quantum computer代考|Comparing backends

The IBM Quantum” backends are all slightly different, from the number of qubits to the individual behavior and interaction between these. Depending on how you write your quantum program, you might want to run the code on a machine with certain characteristics.
The backend information that is returned by IBMQ is just a plain Python list and you can juggle the returned data with any other list. For example, you can write a Python script that finds the available IBM Quantum” backends, then run a quantum program on each of the backends and compare the results in a diagram that shows a rough measure of the quality of the backends’ qubits.

In this recipe, we will use a simple Python loop to run a succession of identical Bell-state quantum programs on the available IBM Quantum” backends to get a rough estimate of the performance of the backends.
The file required for this recipe can be downloaded from here: https://github .com/ PacktPublishing/Quantum-Computing-in-Practice-with-Qiskit-andIBM-Quantum-Experience/blob/master/Chapter05/ch5_r2_comparing_ backends . py.

## 物理代写|量子计算代写Quantum computer代考|Locating the available backends

1. 首先导入所需的类和方法并加载您的帐户信息。在这种情况下，我们使用 IBMQ 类，其中包含主要的硬件相关功能。
2. 查看您的帐户可用的机器。
3. 选择一个普遍可用的后端。
4. 在选定的后端创建并运行贝尔状态量子程序。
5. 选择一个模拟器后端，再次运行贝尔状态量子程序进行比较。
准备
在这个秘籍中，我们将使用 IBMQ 提供者 .backends () 方法来识别和过滤可用的后端来运行您的程序，然后使用 provider.get backend () 方法来选择后端。在下面的示例中，我们将使用 ibmqx2 和 ibmq_qasm_simulator 后端。然后，我们将在其中一个硬件后端上运行一个小型量子程序，然后在模拟器后端上运行。
以下配方中的 Python 文件可以从这里下载：https : // github。com/PacktPublishing/Quantum-Computing-in-Practice-withQiskit-and-IBM-Quantum-Experience/blob/master/Chapter05/ch5_r1_identifying_backends.py。

## 物理代写|量子计算代写Quantum computer代考|Comparing backends

IBM Quantum 的后端都略有不同，从量子比特的数量到个体行为和它们之间的交互。根据您编写量子程序的方式，您可能希望在具有某些特征的机器上运行代码。
IBMQ 返回的后端信息只是一个普通的 Python 列表，您可以将返回的数据与任何其他列表混合使用。例如，您可以编写一个 Python 脚本来查找可用的 IBM Quantum 后端，然后在每个后端上运行一个量子程序，并在图表中比较结果，该图表显示了后端量子比特质量的粗略测量。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Quantum-cheating in a coin toss

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Introducing the Bell state

So, now you have the ability to toss one or more quantum coins and get a probabilistic outcome. That is all well and good, and we could picture ourselves doing some gambling with this new tool of ours, betting money against the outcome of a coin toss. But with a $50 / 50$ outcome, the possibility of earning any real money is limited, unless, of course, we tweak the odds (that is, we cheat).
So how do you cheat in coin tossing? Well, knowing the outcome beforehand would be a clever way. And it turns out this is possible using a quantum phenomenon called entanglement.
By entangling two qubits, we connect them in a way so that they can no longer be described separately. In the most basic sense, if you have two entangled qubits and measure one of them as $|0\rangle$, the result of measuring the other one will be $|0\rangle$ as.
So, how do we use this to cheat in coin tossing? Well, we create two qubits, entangle them, and then we separate them (turns out this is the tricky part to do physically, but we will ignore that for now). You bring one qubit into the gambling den, and your friend keeps the other qubit outside the room.

When it is time to do a coin toss, you run your quantum circuit, entangle the qubits, and then your friend measures the qubit that they keep outside the room. They then sneakily, through some means (such as Bluetooth earphones, semaphoring, or telepathy), tell you what their measurement was, $|0\rangle$ or $|1\rangle$. You will then instantly know what your qubit is, before you measure it, and can bet money on that outcome. After measuring, you will find that you were indeed right, and cash in your winnings.
So, how is this done quantum programmatically? We will introduce a new gate, controlled-NOT $(\mathrm{CX})$.

## 物理代写|量子计算代写Quantum computer代考|More ways to quantum-cheat – tweaking the odds

In the previous recipe, we used a quantum phenomenon called entanglement to cheat with our coin tossing. Admittedly, this might be complicated to set up, and people do tend to get suspicious of coin tossers with an earpiece who are obviously listening for information before catching and revealing the coin (measuring the qubit).

But there are more ways to skin a cat. Remember our discussion of qubits and quantum gates. By manipulating the qubit using gates, we could adjust the state of the qubit before we measure it. The closer the vector is to either $|0\rangle$ or $|1\rangle$, the higher the probability of that specific outcome when you measure.

In this recipe, we will use a rotation gate, the Ry gate, to increase the probability of getting a tails outcome when we toss our coin.
The sample code for this recipe can be found here: https://github.com/ PacktPublishing/Quantum-Computing-in-Practice-with-Qiskit-andIBM-Quantum-Experience/blob/master/Chapter04/ch4_r6_coin_toss_ rot.py .
How to do it…
Set up your code like the previous example and then add a Ry gate to rotate the qubit:

1. Import the classes and methods that we need:
from qiskit import QuantumCircuit, Aer, execute
from qiskit.tools.visualization import plot_histogram
from IPython.core.display import display
from math import pi
2. Set up our quantum circuit with one qubit and one classical bit and create the quantum circuit based on the registers:
$$q c=\text { QuantumCircuit }(1,1)$$

## 物理代写|量子计算代写Quantum computer代考|Adding more coins – straight and cheating

Up until now, our recipes have been mainly of the 1- or 2-qubit sort. With our simulator, there is nothing stopping us from adding more qubits to our circuits at will, with the caveat that each additional qubit will require more and more processing power from the system on which your simulator runs. For example, the IBM Quantum Experience qasm_simulator runs on an IBM POWER9 $9^{\mathrm{m}}$ server and maxes out at around 32 qubits.
In this recipe, we will create two 3 -qubit quantum programs, one multi-coin toss, and one new entangled state called GHZ (for Greenberger-Horne-Zeilinger state).

Instead of doing this by creating two separate files, we will take a look at a new command, reset (). As the name implies, using the reset () command with a qubit sets it back to its original state of $|0\rangle$, ready to start a new quantum computing round. In this example, we use reset () to run two quantum programs in a row, writing to two sets of three classical registers, measuring twice per run.

## 物理代写|量子计算代写Quantum computer代考|More ways to quantum-cheat – tweaking the odds

1. 导入我们需要的类和方法：
from qiskit import QuantumCircuit, Aer, execute
from qiskit.tools.visualization import plot_histogram
from IPython.core.display import display
from math import pi
2. 用一个量子位和一个经典位建立我们的量子电路，并根据寄存器创建量子电路：
qC= 量子电路 (1,1)

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Getting some statistics – tossing many coins in a row

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Getting some statistics – tossing many coins in a row

Alright, so far, we have done a single coin toss at a time, much like you would do in real life.
But the power of quantum computing comes from running your quantum programs many times with the same initial conditions, letting the qubit superpositions play out their quantum mechanical advantages, and summarizing a large number of runs statistically.

With this recipe, we will do 1,000 coin tosses in the blink of an eye and take a look at the results to see how good the coin is. Will this coin be a fair way to start, say, a game of baseball? Let’s see how that works.

The sample code for this recipe can be found here: https://github. com/ PacktPublishing/Quantum-Computing-in-Practice-with-Qiskitand-IBM-Quantum-Experience/blob/master/Chapter04/ch4_r2_coin_ tosses.py.

In this recipe, we will explore and expand on the shots job parameter. This parameter lets you control how many times you run the quantum job cycle – prepare, run, measure. So far, we have prepared our qubits in the $|0\rangle$ state, set the backend to a simulator, and then run one shot, which represents one full cycle.

In the IBM Quantum Experience composer examples, we ran our scores 1,024 times, which is the default. We discovered that the output turned statistical. In this recipe, we will play with a different number of shots to see how the outcomes statistically change.
Generally speaking, you want to increase the number of shots to improve statistical accuracy.

## 物理代写|量子计算代写Quantum computer代考|Implementing an upside-down coin toss

In this recipe, we will tweak our very first quantum program a little bit but still keep it relatively simple. An actual coin can be tossed starting with either heads or tails facing upward. Let’s do another quantum coin toss but with a different starting point, the coin facing tails up. In Dirac notation, we start with our qubit in $|1\rangle$ instead of in $|0\rangle$.
The sample code for this recipe can be found here: https://github. com/ PacktPublishing/Quantum-Computing-in-Practice-with-Qiskit-andIBM-Quantum-Experience/blob/master/Chapter04/ch4_r3_coin_toss_ tails.py.

Just like the previous recipe, this one is almost identical to the first coin toss recipe. Feel free to reuse what you have already created. The only real difference is that we add a new quantum gate, the $\mathbf{X}$ (or NOT) gate.
How to do it…
The following steps are to a large extent identical to the steps from the Quantum coin toss revisited recipe. There are, however, differences depending on the program you are creating, and what Qiskit” components you are using. I will describe these in detail.
Set up your code like the previous example and then add an $\mathrm{X}$ gate to flip the qubit:

1. Import the required Qiskit” classes and methods:
from qiskit import QuantumCircuit, Aer, execute
from qiskit.visualization import plot_histogram
from IPython. core.display import display
Notice how we are not importing the QuantumRegister and
ClassicalRegister methods here like we did before. In this recipe, we will take
a look at a different way of creating your quantum circuit.
2. Create the quantum circuit with 1 qubit and 1 classical bit:
$q c=$ QuantumCircuit $(1,1)$
Here, we are implicitly letting the QuantumCircuit method create the quantum and classical registers in the background; we do not have to explicitly create them. We will refer to these registers by numbers and lists going forward.
3. Add the Hadamard gate, the $\mathrm{X}$ gate, and the measurement gates to the circuit:
qc.x $(0)$ qc.h $(0)$ qc.measure $(0,0)$

## 物理代写|量子计算代写Quantum computer代考|Tossing two coins simultaneously

So far, we have only played with one coin at a time, but there is nothing stopping us from adding more coins. In this recipe, we will add a coin to the simulation, and toss two coins simultaneously. We will do this by adding a second qubit, expanding the number of qubits – two of everything.
The sample code for this recipe can be found here: https://github . com/ PacktPublishing/Quantum-Computing-in-Practice-with-Qiskit-andIBM-Quantum-Experience/blob/master/Chapter04/ch4_r4_two_coin_ toss.py.

Set up your code like the previous example, but with a 2-qubit quantum circuit:

1. Import the classes and methods that we need:
from qiskit import QuantumCircuit, Aer, execute
from qiskit.tools.visualization import plot_histogram
from IPython.core.display import display
2. Set up our quantum circuit with two qubits and two classical bits:
$q c=$ QuantumCircuit $(2,2)$
3. Add the Hadamard gates and the measurement gates to the circuit:
qc $\cdot h([0,1])$
qc. measure $([0,1],[0,1])$
display (qc. draw (‘mpl’))
Note how we are now using lists to reference multiple qubits and multiple bits. For example, we apply the Hadamard gate to qubits 0 and 1 by using $[0,1]$ as input:
Figure $4.14$ – A 2 -qubit quantum coin toss circuit
4. Set the backend to our local simulator:
backend = Aer.get_backend (‘qasm_simulator’)
5. Run the job with one shot:
counts = execute (qc, backend, shots=1). result().
get_counts (qc)
Again, we are using streamlined code as we are only interested in the counts here.

## 物理代写|量子计算代写Quantum computer代考|Implementing an upside-down coin toss

1. 导入所需的 Qiskit” 类和方法：
from qiskit import QuantumCircuit, Aer,
从 qiskit.visualization 执行 import plot_histogram
from IPython。core.display import display
注意我们没有
像以前那样在这里导入 QuantumRegister 和 ClassicalRegister 方法。在这个秘籍中，我们将
看看创建量子电路的另一种方法。
2. 创建具有 1 个量子位和 1 个经典位的量子电路：
qC=量子电路(1,1)
在这里，我们隐含地让 QuantumCircuit 方法在后台创建量子寄存器和经典寄存器；我们不必显式地创建它们。我们将通过数字和列表来引用这些寄存器。
qc.x(0)质量控制(0)质量控制测量(0,0)

## 物理代写|量子计算代写Quantum computer代考|Tossing two coins simultaneously

1. 导入我们需要的类和方法：
from qiskit import QuantumCircuit, Aer, execute
from qiskit.tools.visualization import plot_histogram
from IPython.core.display import display
2. 用两个量子位和两个经典位建立我们的量子电路：
qC=量子电路(2,2)
qc⋅H([0,1])
质量控制。措施([0,1],[0,1])
display (qc.draw (‘mpl’))
注意我们现在如何使用列表来引用多个量子位和多个位。例如，我们通过使用将 Hadamard 门应用于 qubits 0 和 1[0,1]作为输入：
图4.14– 一个 2 量子比特的量子抛硬币电路
4. 将后端设置为我们的本地模拟器：
backend = Aer.get_backend (‘qasm_simulator’)
5. 一次性运行作业：
counts = execute (qc, backend, shot=1)。结果（）。
get_counts (qc)
同样，我们使用的是流线型代码，因为我们只对这里的计数感兴趣。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Starting at the Ground Level with Terra

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Building a Qiskit® quantum program

Generally speaking, there are just a few required building blocks to create a quantum program using Qiskit”. First, you have to set up the required infrastructure and create the quantum circuit (what we call the quantum score in IBM Quantum Experience*). Then, you have to configure a backend to run your quantum program on, and finally execute and retrieve the results of your calculations.

The following section is a summary of the Python building blocks that are required to make up a quantum program.

Listing the required classes, modules, and functions
Qiskit” includes a large number of Python classes, but for our initial foray, we just need the basic ones. These are used to configure each of the components that follow:

• QuantumCircuit: This is used to create the circuit-the program-that you will execute. You will add gates and other components to the circuit.
• QuantumRegister: This represents the qubits that you can use to build your quantum program.
• ClassicalRegister: This represents the classical bits that are used to store the output of your quantum program.
• Aer: This is the Qiskit” simulation layer, which we will discuss in greater detail in Chapter 7, Simulating Quantum Computers with Aer.
• IBMQ: This module is required to execute your quantum programs on actual IBMQ hardware. It includes the tools you need to interact with IBMQ.
• execute: This component lets you run your program by providing the circuit, a backend, and a number of shots.
Working with quantum registers and classical registers
To be able to build your quantum program, you first need to decide how many qubits you want to work with, and how many classical bits you want to include to store your output. You can either set these up explicitly or use the QuantumCircuit class to automatically create the registers.

## 物理代写|量子计算代写Quantum computer代考|Understanding your quantum circuit

The quantum circuit instance that you create will hold the qubits and classical bits. You will manipulate each instance by adding gates.
A quantum program can be assembled by combining more than one quantum circuit. You can, for example, create a circuit that holds the quantum gates and one circuit that holds the measurement gates. You can then add these circuits together to create a main quantum circuit that makes up your quantum program.
Selecting a backend to run on
To be able to execute your quantum program, you must define a backend. A backend can be a local simulator, an IBM Quantum” simulator in the cloud, or actual IBM Quantum” hardware accessed through the cloud.

Initially, we will use the qasm_simulator backend that is included with Qiskit Aer, but we will also run our quantum programs on some of the freely available IBM Quantum” backends.
Running your circuit as a job
You run the quantum program as a job by providing the circuit, a backend, and a number of shots. If you run your quantum programs on IBM Quantum” hardware, you can also include a job monitor to keep track of your place in the queue.
Receiving the results of your job
When your job has run, the results are returned. In these initial recipes, where we use the qasm_simulator backend or the IBM Quantum” hardware, the returned results will be Python dictionaries.

## 物理代写|量子计算代写Quantum computer代考|Quantum coin toss revisited

In this recipe, we will take a closer look at the very first quantum program we created in IBM Quantum Experience – the quantum coin toss. Again, this is arguably the simplest quantum program that still provides real quantum computing value. It demonstrates the probabilistic nature of quantum computing. For a refresher, see Chapter 3, IBM Quantum Experiences $^{*}$ – Quantum Drag and Drop.
In IBM Quantum Experience”, the coin toss program looked like this:

With the quantum coin toss, we will again use the Hadamard gate to create a quantum superposition, and a measurement gate to force the superposition to collapse into one of the two qubit states $|0\rangle$ or $|1\rangle$, representing heads or tails. This time, however, we will create the circuit in Python with Qiskit”, which means that we need to also create the framework for the gates and measurement by defining and creating quantum circuits and classical circuits using Python commands.
This is a quantum circuit that simulates the probabilistic nature of a single qubit in superposition. The 1 -qubit circuit initializes the qubit in the ground state $-|0\rangle-$ and then uses a Hadamard gate to put the qubit in superposition.
During our calculations, the statevector of the qubit looks like this:
$$|\psi\rangle=\frac{|0\rangle+|1\rangle}{\sqrt{2}}$$
Figure $4.2$ – Formula for the statevector of the qubit
You can also write it in the vector form:
$$|\psi\rangle=\left[\begin{array}{c} \frac{1}{\sqrt{2}} \ \frac{1}{\sqrt{2}} \end{array}\right]$$
Figure $4.3$ – Statevector of the qubit in the vector form
Another vector form is the Qiskit” statevector form that you will see in these examples:
$$\left[\begin{array}{lll} 0.70710678+0 . j & 0.70710678+0 . j \end{array}\right]$$
Measuring the qubit causes it to collapse into one of the states $|0\rangle$ or $|1\rangle$ with a $\sim 50 \%$ probability, that is, a coin toss. The result is displayed as a numeric readout, as a bar diagram, and as a Bloch sphere.

## 物理代写|量子计算代写Quantum computer代考|Building a Qiskit® quantum program

Qiskit”包含大量 Python 类，但对于我们最初的尝试，我们只需要基本的类。这些用于配置以下每个组件：

• QuantumCircuit：这用于创建您将执行的电路——程序。您将在电路中添加门和其他组件。
• QuantumRegister：这代表你可以用来构建你的量子程序的量子比特。
• ClassicalRegister：这表示用于存储量子程序输出的经典位。
• Aer：这是 Qiskit 模拟层，我们将在第 7 章用 Aer 模拟量子计算机中更详细地讨论它。
• IBMQ：需要此模块才能在实际 IBMQ 硬件上执行您的量子程序。它包括与 IBMQ 交互所需的工具。
• 执行：此组件允许您通过提供电路、后端和多个镜头来运行程序。
使用量子寄存器和经典寄存器
为了能够构建您的量子程序，您首先需要确定要使用多少量子比特，以及要包含多少经典比特来存储您的输出。您可以显式设置这些，也可以使用 QuantumCircuit 类自动创建寄存器。

## 物理代写|量子计算代写Quantum computer代考|Quantum coin toss revisited

|ψ⟩=|0⟩+|1⟩2

|ψ⟩=[12 12]

[0.70710678+0.j0.70710678+0.j]

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|Tossing a quantum coin

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|Tossing a quantum coin

One of the examples I use is what is arguably the simplest useful quantum program that you can build: a simulated coin toss.
We will go into more detail about the quantum coin toss in Chapter 4, Starting at the Ground Level with Terra, but I will use that program as an example here. It is very small, and not too complicated to understand.
As we discussed briefly in Chapter 2, Quantum Computing and Qubits with Python, a quantum computer, in contrast to a classical computer, provides you with probabilistic, or randomized, computation. In this case, we set up our qubit as a superposition that results in probabilities to get an outcome of 0 or 1 , or heads or tails in coin toss nomenclature, when we measure the qubit.

Build the quantum circuit and then run it. This is the circuit we will come back to later in the book, on the Qiskit” side of things:

1. Log in to IBM Quantum Experience at https: / quantum-computing . ibm. com/composer.
2. From IBM Quantum Experience”, select Circuit Composer from the left pane.
3. Create a new circuit.
4. Find the gates that you need.
In this recipe, we will just use two quantum instructions, one of which we briefly discussed in Chapter 2, Quantum Computing and Qubits with Python, in the Hadamard gate recipe. Remember that the H gate takes the input qubit and creates a superposition.
We will also use a measurement instruction to measure the qubit and write the result to the classical bit line at the bottom of the score.

## 物理代写|量子计算代写Quantum computer代考|Moving between worlds

Now you have seen how to create your quantum scores in Circuit Composer, and how to run them on a simulator, and on a real IBM quantum computer. But the rest of the book will be about working in Qiskit” with your programs. Do we just say farewell to IBM Quantum Experience” then?
Not so fast. IBM Quantum Experience ${ }^{*}$ is a great environment for learning how to build quantum scores, and you do not have to troubleshoot Python code or worry about your environment being up to date (IBM takes care of that for you), and it is actually pretty easy to take what you create in IBM Quantum Experience and just move it over to Qiskit”.
You have two options:

• Qiskit”: With Qiskit” code export, your quantum score is translated into Python code that you can paste directly into your Python interpreter and run. This is a one-way trip from IBM Quantum Experience” to Qiskit”.

## 物理代写|量子计算代写Quantum computer代考|Technical requirements

display (qc.draw (‘mpl’)) 这个例子将量子电路 qc 打印到 iPython 控制台。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|量子计算代写Quantum computer代考|IBM Quantum Experience® – Quantum Drag and Drop

statistics-lab™ 为您的留学生涯保驾护航 在代写量子计算Quantum computer方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写量子计算Quantum computer代写方面经验极为丰富，各种代写量子计算Quantum computer相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|量子计算代写Quantum computer代考|A quick introduction to quantum gates

Now that we have sorted out the difference between bits and qubits, and have also understood how to visualize the qubit as a Bloch sphere, we know all that there is to know about qubits, correct? Well, not quite. A qubit, or for that matter, hundreds or thousands of qubits, is not the only thing you need to make a quantum computer! You need to perform logical operations on and with the qubits. For this, just like a classical computer, we need logical gates.
I will not go into any great detail on how logical gates work, but suffice to say that a quantum gate, operates on the input of one or more qubits and outputs a result.
In this recipe, we will work our way through the mathematical interpretation of few quantum gates by using matrix multiplication of single- and multi-qubit gates. Don’t worry, we will not dig deep, just a little to scratch the surface. You will find a deeper look quantum gates in Chapter 6, Understanding the Qiskit Gate Library.
Again, we will not be building any actual Qiskit quantum circuits just yet. We are still using more or less plain Python with some NumPy matrix manipulations to prove our points.

## 物理代写|量子计算代写Quantum computer代考|Introducing IBM Quantum Experience®

IBM Quantum Experience ${ }^{“}$ is an open platform available for someone to start their quantum computing journey. In it, you have free access to a number of IBM quantum computers, ranging in size from a single qubit to 15 qubits (at the time of writing), as well as a 32 -qubit simulator that runs on IBM POWER9” hardware. That’s a lot of power at your fingertips.
IBM Quantum Experience” opened its doors in May 2016, in a world-first announcement that the public would now have access to actual quantum computing hardware in the cloud. Since then, several other companies have announced similar initiatives and opened up for cloud quantum computing, initially on simulators. Notable among this crowd are Google, Microsoft, Rigetti, Qutech, and more. As of this book’s writing, IBM gives free access to both hardware and software quantum computing through its IBM Quantum Experience”, we will focus on that platform.

You are now on the main IBM Quantum Experience” landing page from which you can access all the quantum experience tools.

From here, you will see the following:

• In the right pane, we have backends that are available to you. Clicking on each brings up a data page with the access status, provider access, chip structure and error rate data, the number of qubits, a list of basis gates, and more.
• In the center area, you find your workbench. There’s a list of recent circuits, currently running experiments, and your previous experiment results; when you first drop in here, it will be quite empty. From this area, you can also manage your user profile, configure notifications, get your API key, and more.
• To the left, we have the main tools and help resources. These are described in more detail in the next section’s How to do it….

## 物理代写|量子计算代写Quantum computer代考|Building quantum scores with Circuit

This recipe will walk you through the basic steps of creating a quantum score in IBM Quantum Experience”, to get a feel for how the composer works, how to build and modify a score, and finally how to analyze the score step by step using the Inspect feature.
Drag-and-drop programming
The recipes in this chapter will be run in the IBM Quantum Experience” web environment, using the drag-and-drop interface, which nicely visualizes what you are doing in an intuitive way.
How to do it…
Let’s build ourselves a little quantum score:

2. In the left pane, select Circuit Composer.
This opens the composer to a blank Untitled circuit.
1. Optional: Set the number of qubits to play with.
In the default setting, you will see three lines, much like a music score (hence the term quantum score). Each line represents one of your qubits, and the basic score is designed for a 5-qubit machine. As you will see in the Comparing backends recipe in Chapter 5, Touring the IBM Quantum “Hardware with Qiskit”, this is currently the most common setup for the free IBM quantum machines.

For this example, we want to use only 1 qubit for clarity. If we use all five, the results that will be displayed will also include the results of the four we won’t be using, which can be confusing.

So, in the Untitled circuit tab that you just opened, hover over a qubit label $\left(\mathbf{q}_{0}\right)$. The label shifts to a trash can icon. Use this icon to remove qubits until you have one left. Your quantum score now has only one line.

## 物理代写|量子计算代写Quantum computer代考|Introducing IBM Quantum Experience®

IBM 量子体验“是一个开放平台，可供人们开始他们的量子计算之旅。在其中，您可以免费访问许多 IBM 量子计算机，大小从单个 qubit 到 15 qubit（在撰写本文时）不等，以及在 IBM POWER9 硬件上运行的 32 qubit 模拟器。触手可及的强大功能。
IBM Quantum Experience”于 2016 年 5 月开业，这是世界上第一次宣布公众现在可以访问云中的实际量子计算硬件。从那时起，其他几家公司也宣布了类似的举措，并开始使用云量子计算，最初是在模拟器上。在这群人中值得注意的是谷歌、微软、Rigetti、Qutech 等。在撰写本书时，IBM 通过其 IBM Quantum Experience 提供了对硬件和软件量子计算的免费访问”，我们将重点关注该平台。

• 在右侧窗格中，我们有可供您使用的后端。单击每个会打开一个数据页面，其中包含访问状态、提供商访问、芯片结构和错误率数据、量子比特数、基础门列表等。
• 在中心区域，您可以找到您的工作台。有一个最近的电路列表，当前正在运行的实验，以及你以前的实验结果；当你第一次来这里时，它会很空。在此区域，您还可以管理您的用户配置文件、配置通知、获取您的 API 密钥等等。
• 在左侧，我们有主要工具和帮助资源。这些将在下一节的如何做……中更详细地描述。

## 物理代写|量子计算代写Quantum computer代考|Building quantum scores with Circuit

1. 从您的 Web 浏览器（Chrome 似乎效果最好），转到以下 URL，然后使用您的 IBM Quantum Experience 帐户登录：https:/quantumcomputing。IBM , com/.
2. 在左侧窗格中，选择 Circuit Composer。
这会将作曲家打开到一个空白的无标题电路。
3. 可选：设置要使用的量子比特数。
在默认设置中，您将看到三行，很像乐谱（因此称为量子乐谱）。每条线代表你的一个量子位，基本分数是为 5 量子位机器设计的。正如您将在第 5 章“使用 Qiskit 浏览 IBM Quantum 硬件”中的比较后端秘籍中看到的，这是目前免费的 IBM 量子机器最常见的设置。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。