### 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⟩

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## MATLAB代写

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