Quantum computing relies on processing of information within a quantum system with many continuous degrees of freedom. The practical implementation of this idea requires complete control over all of the 2 n independent amplitudes of a many-particle wave function, where n >1000. The principles of quantum computing are discussed from the practical point of view, with the conclusion that a working device cannot be built in the foreseeable future.
Quantum computing relies on processing of information within a quantum system with many continuous degrees of freedom. The practical implementation of this idea requires complete control over all of the 2 n independent amplitudes of a many-particle wave function, where n >1000. The principles of quantum computing are discussed from the practical point of view, with the conclusion that a working device cannot be built in the foreseeable future.
We discuss the use of the transverse spatial degrees of freedom of photons propagating in the paraxial approximation for continuous-variable information processing. Given the wide variety of linear optical devices available, a diverse range of operations can be performed on the spatial degrees of freedom of single photons. Here we show how to implement a set of continuous quantum logic gates which allow for universal quantum computation. In contrast with the usual quadratures of the electromagnetic field, the entire set of single-photon gates for spatial degrees of freedom does not require optical nonlinearity and, in principle, can be performed with a single device: the spatial light modulator. Nevertheless, nonlinear optical processes, such as four-wave mixing, are needed in the implementation of two-photon gates. The efficiency of these gates is at present very low; however, small-scale investigations of continuous-variable quantum computation are within the reach of current technology. In this regard, we show how novel cluster states for one-way quantum computing can be produced using spontaneous parametric down-conversion.
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.
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.
Quantum information processing offers fundamental improvements over classical information processing, such as computing power, secure communication, and high-precision measurements. However, the best way to create practical devices is not yet known. This textbook describes the techniques that are likely to be used in implementing optical quantum information processors. After developing the fundamental concepts in quantum optics and quantum information theory, the book shows how optical systems can be used to build quantum computers according to the most recent ideas. It discusses implementations based on single photons and linear optics, optically controlled atoms and solid-state systems, atomic ensembles, and optical continuous variables. This book is ideal for graduate students beginning research in optical quantum information processing. It presents the most important techniques of the field using worked examples and over 120 exercises.
Quantum computing harnesses the mystifying principles of quantum mechanics to address challenges beyond the grasp of traditional computers. This illuminating paper digs far below the theoretical foundations underpinning quantum computing, applicable uses presently explored, and enormous barriers slowing advancement to accomplishing quantum supremacy. Core topics covered profoundly comprise delicate interactions connecting quantum bits, quantum logic gates manipulating superposed states, and algorithms exponentially outpacing usual techniques in cryptography and optimization. The document also surveys recent breakthroughs and maps out the lengthy road still ahead to rendering quantum computing feasible in the genuine world.
Many-body topology is a central concept in modern theories of solids, and identifying effective degrees of freedom that capture it is important both fundamentally and practically. This work studies the extent to which geometric information of an interacting many-body ground state can be inferred from a finite number of local correlations. Starting from the Resta formula, $ z=\left\langle \exp\!\left(\frac{2πi}{L}\hat X\right)\right\rangle$, we view logz as the cumulant generating function and establish a generic information hierarchy across cumulant orders. We show that, for an N-particle system, even complete knowledge of all density correlators up to order N−1 does not, in general, uniquely determine the Berry phase γ=Imlogz(mod2π). In the thermodynamic limit, the statement becomes stronger: no finite set of local correlators suffices to determine the global holonomy. We also identify two exceptional yes-go cases in which the hierarchy is broken. First, for quasi-free models, all cumulants are determined by the particle two-point correlation function. Second, symmetry-enforced constraints can reduce the infinite cumulant sum entering logz to finite information. The argument is analytic and does not rely on a specific microscopic Hamiltonian. Our results clarify a limitation of approaches based on local degrees of freedom for many-body holonomy and provide a minimal framework for distinguishing when global holonomies are encoded in local correlations and when they are not. We also comment on the possibility of analogous hierarchies in other contexts, such as the quantum marginal problem in quantum information theory and many-body scattering problems. Finally, we discuss implications for future numerical work, including machine-learning approaches to the search for topological phases.