Scientific Series

Adiabatic Quantum Computation is not only a possibly more robust alternative to standard quantum computation. Since it considers a continuous-time evolution of the system, it also provides a natural bridge towards studying the dynamics of interacting many-particle quantum systems, quantum phase transitions and other issues in fundamental physics. After a brief review of adiabatic quantum computation, I will show our recent results on the dynamics of entanglement and fidelity for the search and Deutsch algorithms including several variations and optimization. I will show how these studies led to suggesting an alternative definition of entanglement and compare the results, and discuss possible implications for considering entanglement a resource. I will conclude with an outlook on further applications and extensions of adiabatic quantum computation.

Category theory is a general language for describing things and processes - called "objects" and "morphisms". In this language, many counterintuitive features of quantum theory turn out to be properties shared by the category of Hilbert spaces and the category of cobordisms, in which objects are choices of "space" and emorphisms are choices of "spacetime". This striking fact suggests that "n-categories with duals" are a promising language for a quantum theory of spacetime. We sketch the historical development of these ideas from Feynman diagrams to string theory, topological quantum field theory, spin networks and spin foams, and especially recent work on open-closed string theory, 3d quantum gravity coupled to point particles, and 4d BF theory coupled to strings.

It has recently been proposed by Nayeri, Brandenberger and Vafa, that the thermodynamics of strings in the early universe can provide us with a causal mechanism to generate a scale invariant spectrum of primordial density fluctuations, without requiring an intervening epoch of inflation. We will review this mechanism, and report on more recent work which has uncovered several observational consequences of the NBV mechanism, some of which in principle, will be distinguishable from the generic predictions of inflation.

We propose a new brane world scenario. In our model, the Universe starts as a small bulk filled with a dense gas of branes. The bulk is bounded by two orbifold fixed planes. An initial stage of isotropic expansion ends once a weak potential between the orbifold fixed planes begins to dominate, leading to contraction of the extra spatial dimensions. Depending on the form of the potential, one may obtain either a non-inflationary scenario which solves the entropy and horizon problem, or an improved brane-antibrane inflation model.

Clifton, Bub, and Halvorson claim to be able to derive quantum mechanics from information-theoretic axioms. However, their derivation relies on the auxiliary assumption that the relevant probabilities for measurement outcomes can be represented by the observables (self-adjoint operators) and states of a C*-algebra. There are legitimate probability theories that are not so representable --- in particular, the nonlocal boxes of Popescu and Rohrlich. We explain the impact of nonlocal boxes on the interpretation of the CBH derivation, and we discuss possible generalizations of the CBH derivation in the framework of these more general probability theories.

This talk is concerned with the noise-insensitive transmission of quantum information. For this purpose, the sender incorporates redundancy by mapping a given initial quantum state to a messenger state on a larger-dimensional Hilbert space. This encoding scheme allows the receiver to recover part of the initial information if the messenger system is corrupted by interaction with its environment. Our noise model for the transmission leaves a part of the quantum information unchanged, that is, we assume the presence of a noiseless subsystem or of a decoherence-free subspace. We address the case when the noiseless component cannot contain all the quantum information to be transmitted, and investigate how to best spread the information in a quantum state across the noise-susceptible components. (Joint work with David Kribs and Vern Paulsen.)

Nanostructured materials continue to be the focus of intense research due to their promise of innumerable practical applications as well as advancing the fundamental understanding of these intriguing materials. From physics, to chemistry, to biology, to computer science, across the engineering disciplines and into the imagination of the general event, nanotechnology has become an extremely popular buzzword that represents both hope and hype to many people. This talk will outline and describe the exploding field of nanotechnology, including its potential for promising new applications, and for negative societal implications that cause many to fear it. Recent work in our group in the area of integration of nanoscale structures with silicon will be outlined to show the scope and approaches to building nanoscale architectures; the applications of these frameworks include molecular computing, nanoscale sensing platforms, integration of silicon with biology, and intricate structures with unforeseen properties.

We will look at the axioms of quantum mechanics as expressed, for example, in the book by M. A. Nielsen and I. L. Chung ("Quantum Computation and Quantum Information"). We then take a critical look at these axioms, raising several questions as we go. In particular, we will look at the possible informational completeness property of the family of operators that we measure. We will propose physical solutions based on the results of quantum mechanics on phase space and the measurement of quantum particles by quantum mechanical means. We illustrate this with both momentum-position measurements and spin measurements.