MyDigitalWorld10EnglishU1 (10) PDF - Quantum Computing

1 Unit One: Quantum Computing 1 What Comes After Supercomputers? In 2020, the COVID-19 pandemic turned our world upside down. Schools were closed, we were forced to stay at home, and everyone was worried about this new virus. Scientists around the world were wor...

1 Unit One: Quantum Computing 1 What Comes After Supercomputers? In 2020, the COVID-19 pandemic turned our world upside down. Schools were closed, we were forced to stay at home, and everyone was worried about this new virus. Scientists around the world were working day and night to find a vaccine or treatment to stop the virus. But here was the problem-it wasn’t easy to find a cure or vaccine; it involved a lot of really complex science. To find a treatment, scientists had to study an enormous amount of data. They needed to analyze the genetic code of the virus, understand how it spreads, and test how different drugs interact with it. 6  Imagine you have a massive library filled with books, and you need to find specific words in each book, but you only have a few minutes to do it. This was the situation for the scientists-they had a vast amount of data to sort through, but time was running out. Typically, when scientists have a lot of data to analyze, they use computers. However, even the most powerful computers, known as supercomputers, were struggling with this task due to the highly complex data. This problem repeats itself in many fields, as some of the scientific challenges we face today would take decades, even hundreds of years, to solve using classical computing principles, even when applied to supercomputers! Q So, what do you think is the next alternative to classical computing? Discuss this with your teacher and friends. 7 Bits and Information Processing Paths The classical computers we use every day, like our phones, laptops, and school computers, are amazing machines that store and process information using basic units called bits. A bit is the smallest unit of data in a classical computer and is like a tiny switch that can either be off or on, 0 or 1. These computers process information by flipping these bits between off and on in a very specific order. To solve a problem, these computers need to calculate all the possible solutions and execute them step by step, then compare them to find the best possible solution. Example: Jane wants to host three friends for 4x3x2x1=24 lunch at her place. When she thought about arranging the seating at the dining table, she realized that there are 4 factorial (4!) ways to arrange their seats, which means there are 24 possible seating arrangements. 8 When her cousin heard about it, she wanted to join them as well. So now there are 4 guests, and with Jane, the total number is 5. This increases the number of arrangements to 5 factorial (5!), which equals 120. The number increases rapidly! 5! 5x4x3x2x1=120 With the addition of her two cousins and three of her classmates, the number of possible arrangements increases exponentially. With 10 guests, the number of arrangements becomes 10 factorial (10!), which equals 3,628,800. 10! 10x9x8x7x6x5x4x3x2x1=3,628,800 Jane felt overwhelmed! She thought: If I were trying to host 60 guests, the number of possible arrangements would approach the number of atoms in the universe! 9 This type of problem highlights the limitations of classical computing in handling issues that grow increasingly complex, demonstrating how some problems can become unsolvable for classical computers as complexity increases. And this leads us to the problem that classical computers can only do one thing at a time. So, if we have a lot of information to process, they have to go through it step by step, bit by bit. Imagine Jane in a huge maze of arrangements and ideas, and she has to try every possible arrangement to find the way out. If she can only try one path at a time, it might take a long time to find the way out, right? This type of problem is called Optimization Problems. 10 Now, think about the scientists during the COVID-19 pandemic. They needed to find a way out of the maze of information-genetic data, drug interactions, protein structures-all of it. And they didn’t have time to waste. For this reason, and for many problems that came before it and those that will come after, scientists turned to a new method of storing and processing information called qubits. These do not operate on classical computers (even if they are supercomputers) but work on Quantum Computers. Imagine if, instead of evaluating each possible seating arrangement for the guests at the table separately, Jane could represent all possible arrangements at once. This is like Jane having the ability to try all the paths in the maze simultaneously, instead of one at a time. This is exactly what Quantum Computing means. 11 Activity 1: 1 Form a team with one of your friends. 2 Research the meaning of quantum computers that already exist using your preferred search engine. 3 Also, look for the answer to the question, “Can anyone purchase a quantum computer at the present time?” 4 After reviewing several results, summarize your findings and share them with your teacher and classmates. Quantum computers use qubits. Qubits are unique because, unlike classical bits, they can exist in a state called superposition. This means that a qubit can be 0 and 1 at the same time. Think of it as being in two places at once! Not only that, but qubits can also be linked together in a way that allows you to know the state of one qubit instantly if you know the state of the other, no matter how far apart they are. 12 This phenomenon is called entanglement. Thanks to these special properties, quantum computers can process vast amounts of information simultaneously. So, if we used a quantum computer to handle COVID-19 data, it could help find a solution faster by simulating how different drugs interact with the virus much more quickly than classical computers. As a result, scientists could narrow down the list of potential treatments and vaccines more rapidly than they could using other methods. Remember: Quantum computers provide an advantage in problems where solutions can be evaluated in parallel, such as optimization tasks. This advantage doesn’t come from executing individual operations faster, but from reducing the number of operations exponentially to solve complex problems. Quantum computing is still in its early stages, much like classical computers were in the 1940s and 1950s. Modern quantum computers are large, require cooling, and have limited capabilities. However, advancements are ongoing, and quantum computers are expected to complement classical computers in specific tasks in the future. 13 Activity 2: Key Figures in Quantum Computing Just as classical computing had its key figures who contributed to its development, quantum computing also has its pivotal personalities who have worked on it, each contributing in different ways, such as: Richard Feynman: Credited with proposing the concept of quantum computing in the 1980s. Peter Shor: Known for Shor’s algorithm, which demonstrated that quantum computers could break classical encryption. David Deutsch: Contributed to the theoretical foundations of quantum computing and proposed the first quantum algorithm. 1 Form a team with one of your friends. 2 Research the key figures in quantum computing using your preferred search engine. 3 Choose one of the figures and prepare a presentation about them. 4 Present your findings to your teacher and classmates. 14 2 Schrödinger’s Cat In 1935, the Austrian physicist Erwin Schrödinger proposed a thought experiment with the following scenario: 1 A cat is placed inside a sealed box with a few specific elements: a radioactive atom, a Geiger counter (a device for detecting radiation), a vial of poison, and a hammer. The box is then closed so that no one can see what is happening inside. 2 The box is designed so that if the Geiger counter detects radiation (indicating that the radioactive atom has decayed), it activates the hammer to break the vial of poison, killing the cat. If the atom has not decayed, the cat remains alive. 3 The state of the radioactive atom is unknown to anyone observing the box from the outside; it could have decayed or it could not have decayed. 15  4 Similarly, the cat’s state is unknown: it could be dead (if the atom has decayed) or alive (if the atom has not decayed). The atom inside the box is said to be in a "superposition" state, meaning it can be thought of as both decayed and not decayed at the same time until it is observed and measured. The cat is also considered to be in a superposition state, being both "alive" and "dead" at the same time until someone opens the box and observes its state. 5 Observation and Collapse: When the box is opened, the observer forces the system to choose one state, causing the superposition to collapse into a definite outcome: either the cat is alive or dead, but not both Activity 1: This example illustrates the concept of superposition and the measurement problem, both of which are fundamental concepts in quantum computing, which is built on the principles and concepts of quantum mechanics. Have you ever heard of the concept of Quantum Mechanics? Discuss it with your teacher and friends. 16 Quantum computing relies on quantum mechanics, a fundamental branch of physics that describes the behavior of particles at the smallest scales, such as atoms and subatomic particles. Unlike classical physics, which deals with the motion of objects and forces that we can see and interact with directly, quantum mechanics explores phenomena that occur on an extremely small scale, where the rules of physics are entirely different. Key Concepts in Quantum Mechanics 1 Wave-Particle Duality: Particles such as electrons and photons exhibit both wave- like and particle-like properties simultaneously. This means they can spread out like waves while also interacting like discrete particles. 2 Quantization: Many properties, such as energy and angular momentum, can only take on specific, discrete values, known as "quanta." This contrasts with classical physics, where these quantities can change continuously. 17 3 Uncertainty Principle: Formulated by Werner Heisenberg, this principle states that there are fundamental limits to how precisely certain pairs of properties, such as a particle’s position and momentum, can be known. The more accurately one is known, the less precisely the other can be determined. 4 Superposition: Particles can exist in multiple states or locations simultaneously until they are measured or observed. This is clearly illustrated by Schrödinger’s cat thought experiment, where the cat in the box can be both alive and dead at the same time until someone looks inside the box. Similarly, a qubit in quantum computing can be both 0 and 1 at the same time. 5 Entanglement: Particles can become entangled, meaning their states become linked in such a way that the state of one particle instantly affects the state of the other, regardless of the distance between them. This phenomenon puzzled Einstein, who referred to it as "spooky action at a distance." 18 When two qubits become entangled, measuring the state of one immediately determines the state of the other, no matter how far apart they are. For example, if one qubit is measured to be in state |0>, the other qubit will instantly be in state |1>, even if they are separated by great distances. Applications of Quantum Mechanics Quantum mechanics is not just a theory; it has practical applications in various technologies: Transistors and Semiconductors: They form the basis of modern electronics, including computers and smartphones. 19 Lasers: It is used in everything from medical devices to barcode scanners. Magnetic Resonance Imaging (MRI): Magnetic resonance imaging (MRI) in medicine relies on the principles of quantum mechanics to visualize the inside of the human body. 20  Quantum Computing: As mentioned earlier, quantum computing uses the principles of quantum mechanics to perform calculations much faster than traditional computers. Quantum mechanics has radically changed our understanding of nature and continues to drive innovation in science and technology. Activity: 1 Form a team with one of your classmates. 2 Using your preferred search engine, research other potential applications of quantum mechanics. 3 Prepare a presentation and then discuss it with your teacher and classmates. 21 3 Quantum Information Science Kit IBM provides an open-source framework for quantum computing called Qiskit (Quantum Information Science Kit), which allows us to work with quantum computers and quantum algorithms. It also provides tools for writing quantum programs, simulating them on classical devices, and running them on real quantum devices. Qiskit is designed to support research and development in the field of quantum computing by enabling users to design quantum circuits, execute them, and analyze their results. Qiskit consists of: 1 Qiskit Terra: The foundation that allows users to create quantum circuits and define operations on quantum gates. It serves as the basic layer for building quantum programs. 2 Qiskit Aer: Provides high-performance simulators to run experiments locally on classical devices to verify the results before executing them on real quantum devices. 22  3 Qiskit Ignis: A set of tools for quantum error correction and mitigation to enhance the accuracy of quantum computations. 4 Qiskit Aqua: A library of algorithms for quantum applications in chemistry, optimization, machine learning, and more. 5 Qiskit IBMQ: Enables users to run quantum programs on IBM’s real quantum computing devices via cloud access. Activity 1: Installing and Using Qiskit In lesson, we will install and use Qiskit to create a simple quantum circuit that measures the state of a qubit and stores the result in a classical bit. 1 From the terminal command prompt, install Qiskit using the following command: pip install qiskit 23 2 With the help of your teacher, open a new file in Jupyter Notebook. 3 You can also install Qiskit through Jupyter as follows: 24 4 Use this line of code to import all modules and functions from the Qiskit library. It is a quick way to access the tools needed to create quantum circuits, quantum registers, classical registers, and other Qiskit functions. 5 Import the plot_histogram function from the Qiskit. visualization module, which is used to visualize the results of running quantum circuits in the form of graphs. 25 6 The line of code %matplotlib inline ensures that the graphs generated by the matplotlib library are displayed automatically. 7 Create a quantum register called qr that contains one qubit. Quantum registers are used to store qubits, which are the basic units of information in quantum computing. 26 8 Create a classical register called cr that contains one classical bit. Classical registers are used to store classical information (i.e., the results of measurements performed on qubits). 9 This line initializes a quantum circuit called circuit, consisting of the quantum register qr and the classical register cr. The quantum circuit defines the operations (quantum gates, measurements) that will be applied to the qubits and record the results. 27 10 Use the following command to add a measurement operation to the quantum circuit. It measures the qubit in the quantum register qr and stores the result in the classical register cr. In quantum computing, measurement causes the qubit to collapse to either state 0 or 1, and this result is stored in the classical register. The measurement operation in Qiskit has returned an InstructionSet object and stored it at the address 0x264cc3d29e0. It is displayed in this way if you do not explicitly print or display it. 28 Activity 2: Using the Simulator There is more than one way to see the result of the measurement operation in Qiskit, one of which is using Qiskit Aer to simulate quantum devices. 1 Team up with two of your classmates. 2 Search the internet for how to view measurement results in Qiskit using Qiskit Aer. 3 Implement the method and then present the result to your teacher. 29 4 Quantum Algorithms and Their Applications Quantum algorithms are a set of procedures that run on quantum computers, leveraging principles of quantum mechanics, such as superposition, entanglement, and quantum interference, to solve certain computational problems more efficiently than classical algorithms. Here are some of the most well-known quantum algorithms: 1 Shor's Algorithm (for Integer Factorization): Purpose: Shor's algorithm efficiently factors large integers, a task that is computationally difficult for classical computers. Application: It can break encryption systems like RSA, which rely on the difficulty of factoring large prime numbers. If implemented on a sufficiently powerful quantum computer, it could decrypt widely used encryption systems. 30 2 Grover's Algorithm (for Database Search): Purpose: Grover's algorithm provides a quadratic speedup for unstructured search problems, meaning it can find a specific element in an unsorted database faster than classical algorithms. Application: It can be used for searching large databases, solving optimization problems, and finding solutions to NP- hard problems. It has the potential to accelerate various search tasks in artificial intelligence and machine learning. 3 Quantum Fourier Transform (QFT): Purpose: It is the quantum version of the classical Fourier transform and plays a key role in many quantum algorithms, including Shor's algorithm. Application: It is used in signal processing, phase estimation, and cryptographic protocols. 4 Quantum Phase Estimation: Purpose: To determine the eigenvalues of a unitary operator, playing a significant role in many quantum algorithms, such as Shor's algorithm and solving systems of linear equations. Application: It is used in chemistry, materials science, and quantum simulations where understanding quantum phase is essential. 5 Quantum Approximate Optimization Algorithm (QAOA): Purpose: QAOA is a quantum algorithm designed to solve combinatorial optimization problems by approximating the optimal solution. 31  Application: It is used in optimization tasks such as scheduling, traffic flow, logistics, and even in machine learning optimization problems. 6 Variational Quantum Eigensolver (VQE) Algorithm: Purpose: VQE is a hybrid quantum-classical algorithm that estimates the ground state energy of a molecule or system by iteratively minimizing a cost function. Application: It is essential in quantum chemistry for calculating molecular properties, such as energy levels, and is used in drug discovery, materials science, and chemical simulations. 7 Quantum Annealing (D-Wave): Purpose: To solve optimization problems by slowly evolving a quantum system to find the lowest energy configuration for the problem. Application: It is used for optimization tasks in fields such as finance (portfolio optimization), artificial intelligence (training machine learning models), and logistics (supply chain optimization). 8 HHL Algorithm (for Solving Systems of Linear Equations): Purpose: The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm that solves systems of linear equations exponentially faster than classical methods. Application: It has applications in machine learning, optimization, and systems of equations that arise in physics, engineering, and finance. 32 9 Quantum Machine Learning Algorithms: Purpose: To apply quantum algorithms to machine learning tasks such as classification, clustering, and optimization. Application: Examples include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNN), and Quantum Principal Component Analysis (QPCA). These algorithms can be applied to tasks in finance, healthcare, and big data analysis. Activity 1: 1 Form a team with two of your classmates. 2 Together, choose one of the quantum computing algorithms. 3 Research and expand your understanding of it using the internet. 4 Prepare a presentation on the algorithm you chose. 5 Present the presentation in class and listen attentively to the other presentations. 6 After listening to all the presentations, identify your favorite algorithm and tell your teacher the reason. 33 Applications of Quantum Algorithms: Quantum algorithms have applications in many fields due to their ability to solve problems faster or more efficiently than classical algorithms. Some prominent fields include: 1 Cryptography: Shor's algorithm poses a direct threat to the RSA encryption system, while Quantum Key Distribution (QKD) offers new methods for establishing secure communications. 2 Optimization: Algorithms such as Grover's algorithm, QAOA, and quantum annealing are used in optimization tasks such as supply chain management, portfolio optimization, and solving scheduling problems. 34 3 Quantum Chemistry and Drug Discovery: Algorithms like VQE and Quantum Phase Estimation enable the simulation of complex molecular structures and chemical reactions, contributing to drug discovery and materials science. 4 Artificial Intelligence and Machine Learning: Quantum algorithms like QSVM, QNN, and Grover's algorithm can accelerate tasks such as classification, pattern recognition, and optimization in machine learning. 5 Finance: Quantum algorithms can improve financial models, enhance portfolio optimization, and solve complex pricing problems in derivatives and options. 6 Logistics and Traffic Management: Quantum algorithms assist in optimizing routes and managing traffic by providing faster solutions to problems involving multiple variables and constraints. 7 Search and Database Queries: Grover's algorithm can accelerate searches in large, unstructured databases and improve query efficiency. 8 Physics Simulation and Materials Science: Quantum algorithms enable the simulation of physical systems, particularly for studying new materials or understanding complex quantum phenomena that are computationally expensive for classical methods. 35 Activity 2: Quantum algorithms have the potential to revolutionize many industries by solving problems that are impossible for classical computers. Which field do you hope quantum computing will impact the most? 1 Form a team with two of your classmates. 2 Together, choose a field that all three of you are interested in. 3 Research possible quantum computing applications in that field. 4 Prepare a presentation and present it to your teacher and classmates. 36