2019 | Buch

# Quantum Computing: An Applied Approach

verfasst von: Jack D. Hidary

Verlag: Springer International Publishing

2019 | Buch

verfasst von: Jack D. Hidary

Verlag: Springer International Publishing

This book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first work to bring these strands together in an updated manner. This work is suitable for both academic coursework and corporate technical training.

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.

“Quantum Computing will change our world in unexpected ways. Everything technology leaders, engineers and graduate students need is in this book including the methods and hands-on code to program on this novel platform.”

—Eric Schmidt, PhD, Former Chairman and CEO of Google; Founder, Innovation Endeavors

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Abstract

What is a quantum computer? The answer to this question encompasses quantum mechanics (QM), quantum information theory (QIT) and computer science (CS).

Abstract

The possibility that we can leverage quantum mechanics to do computation in new and interesting ways has been hiding in plain sight since the field’s early days; the principles of superposition and entanglement can form the basis of a very powerful form of computation. The trick is to build such a system that we can easily manipulate and measure.

Abstract

In this chapter we will cover qubits and the core set of operators we use to manipulate the state of qubits.

Abstract

Since quantum computing offers an alternative approach to computation, it is logical to consider which classes of problems are now tractable in this new regime that were not thought to be tractable in a classical framework. To do so, let’s consider a range of problem classes.

Abstract

Now that we have covered the essential workings of a quantum computer, let us discuss how we can physically realize these devices. There are many different architectures and designs of gate-based quantum computers each with its own pros and cons. In this chapter we will cover the leading paradigms of quantum computational hardware. Check the book’s online site for updates as the technology is changing rapidly.

Abstract

With the growing interest in quantum computing, there are an increasing number of development libraries and tools for the field. There are development environments and simulators in all the major languages including Python, C/C++, Java and others. A comprehensive list can be found on this book’s website.

Abstract

Two of the most fascinating quantum circuits enable us to transmit information in ways that are not possible in the classical regime. In this chapter, we will learn how to build these two circuits. We will then examine a foundational advance in quantum mechanics, the Bell Inequality.

Abstract

In this chapter, we will walk through a number of fundamental quantum algorithms. We call these algorithms the canon as they were all developed in the early years of quantum computing and were the first to establish provable computational speedups with quantum computers. We discussed most of these algorithms at a high level in chapter 2; we will now walk through them in a more detailed manner. A number of these algorithms require a quantum computer that is still in the future, but by analyzing them now we can deepen our understanding of what will be possible. Additionally, variants of these algorithms can be used to prove advantages with near-term quantum computers in the noiseless [47] and even noisy [48] regimes.

Abstract

In this section we will walk through a range of quantum computing programs that can be run on NISQ processors. We will cover methods in optimization, chemistry, machine learning and other areas.

Abstract

In this work, we have taken a journey through the quantum computing landscape; we have explored its theoretical foundation, discussed the key research and milestones that advanced the field and covered a range of hardware approaches and quantum computing methods.

Abstract

One of the most important discoveries of quantum mechanics in the twentieth century was the observation by John von Neumann in his Mathematical Foundations of Quantum Mechanics that all of quantum mechanics can be described by linear algebra [225].

Abstract

We claimed earlier that every linear transformation has an associated matrix, and vice versa. We aim to demonstrate for you that, in fact, a linear transformation and a matrix are the same thing. This justifies the study of linear algebra as the study of matrices and operations on them.

Abstract

Cartesian products and functions are discussed in chapter 11, if you want to brush up on these terms. Boolean functions arise naturally in computing. For example, the Deutsch-Jozsa Algorithm discussed in chapter 7 involves the four Boolean functions.