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Book Quantum Computing for Programmers

Download or read book Quantum Computing for Programmers written by Robert Hundt and published by Cambridge University Press. This book was released on 2022-03-31 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Takes readers from the basics to detailed derivations and open-source implementations of more than 25 fundamental quantum algorithms.

Book Programming Quantum Computers

Download or read book Programming Quantum Computers written by Eric R. Johnston and published by O'Reilly Media. This book was released on 2019-07-03 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers are poised to kick-start a new computing revolution—and you can join in right away. If you’re in software engineering, computer graphics, data science, or just an intrigued computerphile, this book provides a hands-on programmer’s guide to understanding quantum computing. Rather than labor through math and theory, you’ll work directly with examples that demonstrate this technology’s unique capabilities. Quantum computing specialists Eric Johnston, Nic Harrigan, and Mercedes Gimeno-Segovia show you how to build the skills, tools, and intuition required to write quantum programs at the center of applications. You’ll understand what quantum computers can do and learn how to identify the types of problems they can solve. This book includes three multichapter sections: Programming for a QPU—Explore core concepts for programming quantum processing units, including how to describe and manipulate qubits and how to perform quantum teleportation. QPU Primitives—Learn algorithmic primitives and techniques, including amplitude amplification, the Quantum Fourier Transform, and phase estimation. QPU Applications—Investigate how QPU primitives are used to build existing applications, including quantum search techniques and Shor’s factoring algorithm.

Book Practical Quantum Computing for Developers

Download or read book Practical Quantum Computing for Developers written by Vladimir Silva and published by Apress. This book was released on 2018-12-12 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Write algorithms and program in the new field of quantum computing. This book covers major topics such as the physical components of a quantum computer: qubits, entanglement, logic gates, circuits, and how they differ from a traditional computer. Also, Practical Quantum Computing for Developers discusses quantum computing in the cloud using IBM Q Experience including: the composer, quantum scores, experiments, circuits, simulators, real quantum devices, and more. You’ll be able to run experiments in the cloud on a real quantum device. Furthermore, this book shows you how to do quantum programming using the QISKit (Quantum Information Software Kit), Python SDK, and other APIs such as QASM (Quantum Assembly). You’ll learn to write code using these languages and execute it against simulators (local or remote) or a real quantum computer provided by IBM’s Q Experience. Finally, you’ll learn the current quantum algorithms for entanglement, random number generation, linear search, integer factorization, and others. You’ll peak inside the inner workings of the Bell states for entanglement, Grover’s algorithm for linear search, Shor’s algorithm for integer factorization, and other algorithms in the fields of optimization, and more. Along the way you’ll also cover game theory with the Magic Square, an example of quantum pseudo-telepathy where parties sharing entangled states can be observed to have some kind of communication between them. In this game Alice and Bob play against a referee. Quantum mechanics allows Alice and Bob to always win! By the end of this book, you will understand how this emerging technology provides massive parallelism and significant computational speedups over classical computers, and will be prepared to program quantum computers which are expected to replace traditional computers in the data center. What You Will LearnUse the Q Experience Composer, the first-of-its-kind web console to create visual programs/experiments and submit them to a quantum simulator or real device on the cloud Run programs remotely using the Q Experience REST API Write algorithms that provide superior performance over their classical counterparts Build a Node.js REST client for authenticating, listing remote devices, querying information about quantum processors, and listing or running experiments remotely in the cloud Create a quantum number generator: The quintessential coin flip with a quantum twist Discover quantum teleportation: This algorithm demonstrates how the exact state of a qubit (quantum information) can be transmitted from one location to another, with the help of classical communication and quantum entanglement between the sender and receiver Peek into single qubit operations with the classic game of Battleships with a quantum twist Handle the counterfeit coin problem: a classic puzzle that consists of finding a counterfeit coin in a beam balance among eight coins in only two turns Who This Book Is For Developers and programmers interested in this new field of computing.

Book Learn Quantum Computing with Python and Q

Download or read book Learn Quantum Computing with Python and Q written by Sarah C. Kaiser and published by Simon and Schuster. This book was released on 2021-07-27 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn Quantum Computing with Python and Q# introduces quantum computing from a practical perspective. Summary Learn Quantum Computing with Python and Q# demystifies quantum computing. Using Python and the new quantum programming language Q#, you’ll build your own quantum simulator and apply quantum programming techniques to real-world examples including cryptography and chemical analysis. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Quantum computers present a radical leap in speed and computing power. Improved scientific simulations and new frontiers in cryptography that are impossible with classical computing may soon be in reach. Microsoft’s Quantum Development Kit and the Q# language give you the tools to experiment with quantum computing without knowing advanced math or theoretical physics. About the book Learn Quantum Computing with Python and Q# introduces quantum computing from a practical perspective. Use Python to build your own quantum simulator and take advantage of Microsoft’s open source tools to fine-tune quantum algorithms. The authors explain complex math and theory through stories, visuals, and games. You’ll learn to apply quantum to real-world applications, such as sending secret messages and solving chemistry problems. What's inside The underlying mechanics of quantum computers Simulating qubits in Python Exploring quantum algorithms with Q# Applying quantum computing to chemistry, arithmetic, and data About the reader For software developers. No prior experience with quantum computing required. About the author Dr. Sarah Kaiser works at the Unitary Fund, a non-profit organization supporting the quantum open-source ecosystem, and is an expert in building quantum tech in the lab. Dr. Christopher Granade works in the Quantum Systems group at Microsoft, and is an expert in characterizing quantum devices. Table of Contents PART 1 GETTING STARTED WITH QUANTUM 1 Introducing quantum computing 2 Qubits: The building blocks 3 Sharing secrets with quantum key distribution 4 Nonlocal games: Working with multiple qubits 5 Nonlocal games: Implementing a multi-qubit simulator 6 Teleportation and entanglement: Moving quantum data around PART 2 PROGRAMMING QUANTUM ALGORITHMS IN Q# 7 Changing the odds: An introduction to Q# 8 What is a quantum algorithm? 9 Quantum sensing: It’s not just a phase PART 3 APPLIED QUANTUM COMPUTING 10 Solving chemistry problems with quantum computers 11 Searching with quantum computers 12 Arithmetic with quantum computers

Book Foundations of Quantum Programming

Download or read book Foundations of Quantum Programming written by Mingsheng Ying and published by Elsevier. This book was released on 2024-04-29 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers promise dramatic advantages in processing speed over currently available computer systems. Quantum computing offers great promise in a wide variety of computing and scientific research, including Quantum cryptography, machine learning, computational biology, renewable energy, computer-aided drug design, generative chemistry, and any scientific or enterprise application that requires computation speed or reach beyond the limits of current conventional computer systems. Foundations of Quantum Programming, Second Edition discusses how programming methodologies and technologies developed for current computers can be extended for quantum computers, along with new programming methodologies and technologies that can effectively exploit the unique power of quantum computing. The Second Edition includes two new chapters describing programming models and methodologies for parallel and distributed quantum computers. The author has also included two new chapters to introduce Quantum Machine Learning and its programming models – parameterized and differential quantum programming. In addition, the First Edition's preliminaries chapter has been split into three chapters, with two sections for quantum Turing machines and random access stored program machines added to give the reader a more complete picture of quantum computational models. Finally, several other new techniques are introduced in the Second Edition, including invariants of quantum programs and their generation algorithms, and abstract interpretation of quantum programs. - Demystifies the theory of quantum programming using a step-by-step approach - Includes methodologies, techniques, and tools for the development, analysis, and verification of quantum programs and quantum cryptographic protocols - Covers the interdisciplinary nature of quantum programming by providing preliminaries from quantum mechanics, mathematics, and computer science, and pointing out its potential applications to quantum engineering and physics - Presents a coherent and self-contained treatment that will be valuable for academic and industrial researchers and developers - Adds new developments such as parallel and distributed quantum programming; and introduces several new program analysis techniques such as invariants generation and abstract interpretation

Book Automatic Quantum Computer Programming

Download or read book Automatic Quantum Computer Programming written by Lee Spector and published by Springer Science & Business Media. This book was released on 2004-06-11 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automatic Quantum Computer Programming provides an introduction to quantum computing for non-physicists, as well as an introduction to genetic programming for non-computer-scientists. The book explores several ways in which genetic programming can support automatic quantum computer programming and presents detailed descriptions of specific techniques, along with several examples of their human-competitive performance on specific problems. Source code for the author’s QGAME quantum computer simulator is included as an appendix, and pointers to additional online resources furnish the reader with an array of tools for automatic quantum computer programming.

Book Quantum Computing in Action

Download or read book Quantum Computing in Action written by Johan Vos and published by Simon and Schuster. This book was released on 2022-02-08 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computing is on the horizon, ready to impact everything from scientific research to encryption and security. But you don't need a physics degree to get started in quantum computing. Quantum Computing for Developers shows you how to leverage your existing Java skills into writing your first quantum software so you're ready for the revolution. Rather than a hardware manual or academic theory guide, this book is focused on practical implementations of quantum computing algorithms. Using Strange, a Java-based quantum computer simulator, you'll go hands-on with quantum computing's core components including qubits and quantum gates as you write your very first quantum code. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications.

Book Quantum Computing  An Applied Approach

Download or read book Quantum Computing An Applied Approach written by Jack D. Hidary and published by Springer Nature. This book was released on 2021-09-29 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training. The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition. This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates. Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X.

Book Programming the Universe

Download or read book Programming the Universe written by Seth Lloyd and published by Vintage. This book was released on 2007-03-13 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is the universe actually a giant quantum computer? According to Seth Lloyd, the answer is yes. All interactions between particles in the universe, Lloyd explains, convey not only energy but also information–in other words, particles not only collide, they compute. What is the entire universe computing, ultimately? “Its own dynamical evolution,” he says. “As the computation proceeds, reality unfolds.” Programming the Universe, a wonderfully accessible book, presents an original and compelling vision of reality, revealing our world in an entirely new light.

Book Quantum Computing

    Book Details:
  • Author : National Academies of Sciences, Engineering, and Medicine
  • Publisher : National Academies Press
  • Release : 2019-04-27
  • ISBN : 030947969X
  • Pages : 273 pages

Download or read book Quantum Computing written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2019-04-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics, the subfield of physics that describes the behavior of very small (quantum) particles, provides the basis for a new paradigm of computing. First proposed in the 1980s as a way to improve computational modeling of quantum systems, the field of quantum computing has recently garnered significant attention due to progress in building small-scale devices. However, significant technical advances will be required before a large-scale, practical quantum computer can be achieved. Quantum Computing: Progress and Prospects provides an introduction to the field, including the unique characteristics and constraints of the technology, and assesses the feasibility and implications of creating a functional quantum computer capable of addressing real-world problems. This report considers hardware and software requirements, quantum algorithms, drivers of advances in quantum computing and quantum devices, benchmarks associated with relevant use cases, the time and resources required, and how to assess the probability of success.

Book Quantum Computing

Download or read book Quantum Computing written by Eleanor G. Rieffel and published by MIT Press. This book was released on 2011-03-04 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough exposition of quantum computing and the underlying concepts of quantum physics, with explanations of the relevant mathematics and numerous examples.

Book Introducing Microsoft Quantum Computing for Developers

Download or read book Introducing Microsoft Quantum Computing for Developers written by Johnny Hooyberghs and published by Apress. This book was released on 2021-12-10 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dive in with this hands-on introduction to quantum computing with the Microsoft Quantum Development Kit and Q# for software developers. You may have heard about quantum computing, but what does it mean to you as a software developer? With many new developments, a resurgence in interest, and investment by some of the largest tech companies in the world to be the first to market with quantum programming (QP) hardware and platforms, it is no longer a tool in the distant future. Developers are at the forefront, now able to create applications that take advantage of QP through simulations. While the skill is of interest, for many developers, quantum computing and its implications still remains a mystery. In this book, you will get up to speed exploring important quantum concepts and apply them in practice through writing actual quantum algorithms, using the Microsoft Quantum Development Kit. Theoretical knowledge about quantum physics, such as superposition and entanglement, will be used to explain quantum computing topics, including quantum gates, quantum circuits, and quantum algorithms. Finally, take a tour of the new Azure Quantum. Use Q#, Microsoft's new programming language, to target quantum hardware. You will select your supporting language of choice, either C# or Python, to begin writing your quantum applications. Combined with just enough theoretical preparation, you will learn how to get your computer ready to simulate basic quantum programs using Microsoft Visual Studio or Visual Studio Code and Q#. What You Will Learn Get up to speed on the platform-independent quantum tool set using the Microsoft Quantum Development Kit simulator and Visual Studio Code or Microsoft Visual Studio Know the basics of quantum mechanics required to start working on quantum computing Understand mathematical concepts such as complex numbers, trigonometry, and linear algebra Install the Microsoft Quantum Development Kit on a Windows or Linux PC with Visual Studio Code or Microsoft Visual Studio Write quantum algorithms with the Microsoft Quantum Development Kit and Q#, supported by C# or Python Discover insights on important existing quantum algorithms such as Deutch, Deutch-Jozsa, and the fun CHSH-game Get introduced to quantum as a service using the Microsoft Azure Quantum preview cloud offering Who This Book Is For Developers who are interested in quantum computing, specifically those software developers who are planning on using quantum computers in the future. Basic imperative programming knowledge is useful to understand the syntax and structure found in the Q# programming language. Knowledge of Microsoft C# or Python is not required since these languages are only used to support the simulation of Q# on a classical computer.

Book Quantum Computing for Everyone

Download or read book Quantum Computing for Everyone written by Chris Bernhardt and published by MIT Press. This book was released on 2019-03-19 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader. Quantum computing is a beautiful fusion of quantum physics and computer science, incorporating some of the most stunning ideas from twentieth-century physics into an entirely new way of thinking about computation. In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means. Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement—which, he says, is easier to describe mathematically than verbally—and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as “spooky action at a distance”); and introduces quantum cryptography. He recaps standard topics in classical computing—bits, gates, and logic—and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.

Book Quantum Computing

    Book Details:
  • Author : Nihal Mehta P. D.
  • Publisher :
  • Release : 2020-08
  • ISBN : 9781680507201
  • Pages : 582 pages

Download or read book Quantum Computing written by Nihal Mehta P. D. and published by . This book was released on 2020-08 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: You've heard that quantum computing is going to change the world. Now you can check it out for yourself. Learn how quantum computing works, and write programs that run on the IBM Q quantum computer, one of the world's first functioning quantum computers. Learn a simple way to apply quantum mechanics to computer programming. Create algorithms to solve intractable problems for classical computers, and discover how to explore the entire problem space at once to determine the optimal solution. Get your hands on the future of computing today. Quantum computing overhauls computer science. Problems such as designing life-saving drugs and super-large logistics problems that have been difficult or impossible for classical computers to handle can now be solved in moments. Quantum computing makes it possible to explore all possible solutions simultaneously and determine those that work, instead of iterating through each possibility sequentially. Work with quantum computers directly, instead of talking about them theoretically. Work with qubits, the fundamental elements of quantum computing. Discover what makes them different from classical bits. Model complex problems with logic gates specific to quantum computing. Learn how quantum mechanics offers ways to write programs that explore all solutions simultaneously. Create quantum circuits to solve problems that classical computers struggle with. Dive into quantum optimization and cryptography. Use the IBM Q quantum computer to both simulate quantum effects, and actually run your programs on a real quantum machine. Get a head start on the technology that will drive computer science into the future. What You Need: Access to the IBM quantum computer, via any internet connection

Book Quantum Computing with Silq Programming

Download or read book Quantum Computing with Silq Programming written by Srinjoy Ganguly and published by Packt Publishing Ltd. This book was released on 2021-04-30 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the mathematics behind quantum computing and explore the high-level quantum language Silq to take your quantum programming skills to the next level Key FeaturesHarness the potential of quantum computers more effectively using SilqLearn how to solve core problems that you may face while writing quantum programsExplore useful quantum applications such as cryptography and quantum machine learningBook Description Quantum computing is a growing field, with many research projects focusing on programming quantum computers in the most efficient way possible. One of the biggest challenges faced with existing languages is that they work on low-level circuit model details and are not able to represent quantum programs accurately. Developed by researchers at ETH Zurich after analyzing languages including Q# and Qiskit, Silq is a high-level programming language that can be viewed as the C++ of quantum computers! Quantum Computing with Silq Programming helps you explore Silq and its intuitive and simple syntax to enable you to describe complex tasks with less code. This book will help you get to grips with the constructs of the Silq and show you how to write quantum programs with it. You’ll learn how to use Silq to program quantum algorithms to solve existing and complex tasks. Using quantum algorithms, you’ll also gain practical experience in useful applications such as quantum error correction, cryptography, and quantum machine learning. Finally, you’ll discover how to optimize the programming of quantum computers with the simple Silq. By the end of this Silq book, you’ll have mastered the features of Silq and be able to build efficient quantum applications independently. What you will learnIdentify the challenges that researchers face in quantum programmingUnderstand quantum computing concepts and learn how to make quantum circuitsExplore Silq programming constructs and use them to create quantum programsUse Silq to code quantum algorithms such as Grover's and Simon’sDiscover the practicalities of quantum error correction with SilqExplore useful applications such as quantum machine learning in a practical wayWho this book is for This Silq quantum computing book is for students, researchers, and scientists looking to learn quantum computing techniques and software development. Quantum computing enthusiasts who want to explore this futuristic technology will also find this book useful. Beginner-level knowledge of any programming language as well as mathematical topics such as linear algebra, probability, complex numbers, and statistics is required.

Book Learn Quantum Computing with Python and IBM Quantum Experience

Download or read book Learn Quantum Computing with Python and IBM Quantum Experience written by Robert Loredo and published by Packt Publishing Ltd. This book was released on 2020-09-28 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step guide to learning the implementation and associated methodologies in quantum computing with the help of the IBM Quantum Experience, Qiskit, and Python that will have you up and running and productive in no time Key FeaturesDetermine the difference between classical computers and quantum computersUnderstand the quantum computational principles such as superposition and entanglement and how they are leveraged on IBM Quantum Experience systemsRun your own quantum experiments and applications by integrating with QiskitBook Description IBM Quantum Experience is a platform that enables developers to learn the basics of quantum computing by allowing them to run experiments on a quantum computing simulator and a real quantum computer. This book will explain the basic principles of quantum mechanics, the principles involved in quantum computing, and the implementation of quantum algorithms and experiments on IBM's quantum processors. You will start working with simple programs that illustrate quantum computing principles and slowly work your way up to more complex programs and algorithms that leverage quantum computing. As you build on your knowledge, you'll understand the functionality of IBM Quantum Experience and the various resources it offers. Furthermore, you'll not only learn the differences between the various quantum computers but also the various simulators available. Later, you'll explore the basics of quantum computing, quantum volume, and a few basic algorithms, all while optimally using the resources available on IBM Quantum Experience. By the end of this book, you'll learn how to build quantum programs on your own and have gained practical quantum computing skills that you can apply to your business. What you will learnExplore quantum computational principles such as superposition and quantum entanglementBecome familiar with the contents and layout of the IBM Quantum ExperienceUnderstand quantum gates and how they operate on qubitsDiscover the quantum information science kit and its elements such as Terra and AerGet to grips with quantum algorithms such as Bell State, Deutsch-Jozsa, Grover's algorithm, and Shor's algorithmHow to create and visualize a quantum circuitWho this book is for This book is for Python developers who are looking to learn quantum computing and put their knowledge to use in practical situations with the help of IBM Quantum Experience. Some background in computer science and high-school-level physics and math is required.

Book Fundamentals of Quantum Programming in IBM s Quantum Computers

Download or read book Fundamentals of Quantum Programming in IBM s Quantum Computers written by Weng-Long Chang and published by Springer Nature. This book was released on 2020-12-21 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces major topics that include quantum bits, superposition, entanglement, logic gates, quantum search algorithm, quantum Fourier transform, inverse quantum Fourier transform, Shor’s order-finding algorithm and phase estimation. Everyone can write algorithms and programs in the cloud making using IBM’s quantum computers that support IBM Q Experience which contains the composer, open quantum assembly language, simulators and real quantum devices. Furthermore, this book teaches you how to use open quantum assembly language to write quantum programs for dealing with complex problems. Through numerous examples and exercises, readers will learn how to write a quantum program with open quantum assembly language for solving any problem from start to complete. This book includes six main chapters: ·Quantum Bits and Quantum Gates—learn what quantum bits are, how to declare and measure them, what quantum gates are and how they work on a simulator or a real device in the cloud. ·Boolean Algebra and its Applications—learn how to decompose CCNOT gate into six CNOT gates and nine gates of one bit and how to use NOT gates, CNOT gates and CCNOT gates to implement logic operations including NOT, OR, AND, NOR, NAND, Exclusive-OR (XOR) and Exclusive-NOR (XNOR). ·Quantum Search Algorithm and its Applications—learn core concepts of quantum search algorithm and how to write quantum programs to implement core concepts of quantum search algorithm for solving two famous NP-complete problems that are the satisfiability problem in n Boolean variables and m clauses and the clique problem in a graph with n vertices and q edges. ·Quantum Fourier Transform and its Applications—learn core concepts of quantum Fourier transform and inverse quantum Fourier transform and how to write quantum programs to implement them for solving two real applications that are to compute the period and the frequency of two given oracular functions. ·Order-Finding and Factoring—learn core concepts of Shor’s order-finding algorithm and how to write quantum programs to implement Shor’s order-finding algorithm for completing the prime factorization to 15. Phase Estimation and its Applications—learn core concepts of phase estimation and quantum counting and how to write quantum programs to implement them to compute the number of solution(s) in the independent set problem in a graph with two vertices and one edge.