The Quantum Frontier

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.Comment: Invited book chapter for Computation for Humanity - Information Technology to Advance Society to be published by CRC Press. Concepts clarified and style made more uniform in version 2. Many thanks to the referees for their suggestions for improvement

Fault tolerance for holonomic quantum computation

We review an approach to fault-tolerant holonomic quantum computation on stabilizer codes. We explain its workings as based on adiabatic dragging of the subsystem containing the logical information around suitable loops along which the information remains protected.Comment: 16 pages, this is a chapter in the book "Quantum Error Correction", edited by Daniel A. Lidar and Todd A. Brun, (Cambridge University Press, 2013), at http://www.cambridge.org/us/academic/subjects/physics/quantum-physics-quantum-information-and-quantum-computation/quantum-error-correctio

Demonstration of unconditional one-way quantum computations for continuous variables

Quantum computing promises to exploit the laws of quantum mechanics for processing information in ways fundamentally different from today's classical computers, leading to unprecedented efficiency. One-way quantum computation, sometimes referred to as the cluster model of quantum computation, is a very promising approach to fulfil the capabilities of quantum information processing. The cluster model is realizable through measurements on a highly entangled cluster state with no need for controlled unitary evolutions. Here we demonstrate unconditional one-way quantum computation experiments for continuous variables using a linear cluster state of four entangled optical modes. We implement an important set of quantum operations, linear transformations, in the optical phase space through one-way computation. Though not sufficient, these are necessary for universal quantum computation over continuous variables, and in our scheme, in principle, any such linear transformation can be unconditionally and deterministically applied to arbitrary single-mode quantum states.Comment: 9 pages, 3 figure

Prolegomena to a non-equilibrium quantum statistical mechanics

We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium quantum statistical phenomena. As an application, we discuss the non-equilibrium quantum thermodynamics of black hole formation and evaporation.Comment: 20 pages, LaTeX with elsart.cls, 8 postscript figures. Special issue on quantum computation of Chaos, Solitons, and Fractal