Abstract We arrive at the centennial of modern quantum mechanics. In about the last third of that century, we have been busy connecting quantum theory with the theory of information and the theory of computing, and with trying to turn quantum phenomena into quantum technologies. We have been talking about the quantum computer for most this trimester (i.e. for the last third-century of the history of quantum physics). Where are we at with this fantastic device? Here I give a few reflections on this question.
Abstract We arrive at the centennial of modern quantum mechanics. In about the last third of that century, we have been busy connecting quantum theory with the theory of information and the theory of computing, and with trying to turn quantum phenomena into quantum technologies. We have been talking about the quantum computer for most this trimester (i.e. for the last third-century of the history of quantum physics). Where are we at with this fantastic device? Here I give a few reflections on this question.
It is now roughly thirty years since the incipient ideas on quantum information science was concretely formalized. Over the last three decades, there has been much development in this field, and at least one technology, namely devices for quantum cryptography, is now commercialized. Yet, the holy grail of a workable quantum computing machine still lies faraway at the horizon. In any case, it took nearly several centuries before the vacuum tubes were invented after the first mechanical calculating were constructed, and several decades later, for the transistor to bring the current computer technology to fruition. In this review, we provide a short survey of the current development and progress in quantum information science. It clearly does not do justice to the amount of work in the past thirty years. Nevertheless, despite the modest attempt, this review hopes to induce younger researchers into this exciting field.
The development of technology and our understanding of the physical world are necessarily deeply intertwined. New understanding in physics leads to the development of new technology, which in turn provides both new tools for studying the physical world, and new challenges for physicists wishing to improve on this technology. In this sense, the impact over the last century of quantum mechanics — the physics of microscopic particles and systems — has been extreme. In the last two decades alone the explosion of technology based on lasers and semiconductor electronics has been staggering, and these devices are now not only central to our daily lives (in the form of computers, entertainment systems, and medical and industrial equipment), but are also important tools in all branches of physics.
A classical simulation of quantum systems demands enormous computational resources. The dimension of underlying Hilbert space scales exponentially with the number of participating elements ( N ), requiring a 2 2N size of calculation matrix for a unitary operation, for example, 2 100 ≈ 10 30 for only N = 50. With the increase of N , the first obstacle to encounter is in fact the deficiency of computer memories. A straightforward resolution is to use a quantum computer, a calculating device that operates with the principle of quantum mechanics. During the last twenty years, quantum computing once considered as theoretical exercise has become an important field of research in modern physics. At the forefront of quantum information technology, quantum computing has emerged as a new engineering field with broad interest not only in physics but also in computer science, electronics engineering, and mathematics.
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool. This review is about to tell the story of theoretical quantum computation. I left out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review I make these connections explicit, discussing the possible implications of quantum computation on fundamental physical questions, such as the transition from quantum to classical physics.
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.