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

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• 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

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## MATLAB代写

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