We will define the common terms and concepts used in quantum algorithms literature. Here, we provide a self-contained description of the quantum computing programming model. 1.1 The Quantum Computing Programming Model The code and implementations accompanying the article can be found at. Other cloud service-based quantum computers are also available from Rigetti and IonQ, but in this review, we will focus solely on IBM’s quantum computing ecosystem. Other surveys of quantum algorithms with a different target audience and also without actual implementations include. Since real quantum computers, such as IBM Q, are now available as a cloud service, we present results from simulator and actual hardware experiments for smaller input datasets. In this review, we provide a self-contained, succinct description of quantum computing, and of the basic quantum algorithms with a focus on implementation. It is also dominated by physics and algebraic notations that at times present unnecessary entry barriers for mainstream computer scientists and other more mathematically trained scientists. The quantum programming model is fundamentally different from traditional computer programming. We believe the time has come to make quantum algorithms and their implementations accessible to a broad swath of researchers and developers across computer science, software engineering, and other fields. While the mathematical basis of quantum computing, the programming model, and most quantum algorithms have been published decades ago (starting in the 1990s), they have been of interest only to a small dedicated community. (See for a precise technical definition of quantum supremacy.) Nonetheless, this is a watershed moment for quantum computing and is widely seen as an important step on the road toward building quantum computers that will offer practical speedups when solving real-world problems. The problem tackled here by the quantum computer is not one with any direct real-world application. Recently, Google announced that it has reached a major milestone known as quantum supremacy-the demonstration that a quantum computer can perform a calculation that is intractable on a classical supercomputer. These potential advantages, steady advances in nano-manufacturing, and the slow-down of traditional hardware scaling laws (such as Moore’s Law) have led to a substantial commercial and national-security interest and investment in quantum computing technology in the 2010s. Compared to traditional, digital computing, quantum computing offers the potential to dramatically reduce both execution time and energy consumption. Quantum computing exploits quantum-mechanical effects-in particular, superposition, entanglement, and quantum tunneling-to more efficiently execute a computation. Skip 1INTRODUCTION Section 1 INTRODUCTION This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers.
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