Colloquium

The Achilles\\\' heel of quantum information processors is the fragility of quantum states and processes. Without a method to control imperfection and imprecision of quantum devices, the probability that a quantum computation succeed will decrease exponentially in the number of gates it requires. In the last ten years, building on the discovery of quantum error correction, accuracy threshold theorems were proved showing that error can be controlled using a reasonable amount of resources as long as the error rate is smaller than a certain threshold. We thus have a scalable theory describing how to control quantum systems. I will briefly review some of the assumptions of the accuracy threshold theorems and comment on experiments that have been done and should be done to turn quantum error correction into an experimental reality.

The basic problem of much of condensed matter and high energy physics, as well as quantum chemistry, is to find the ground state properties of some Hamiltonian. Many algorithms have been invented to deal with this problem, each with different strengths and limitations. Ideas such as entanglement entropy from quantum information theory and quantum computing enable us to understand the difficulty of various problems. I will discuss recent results on area laws and use these to prove that we can use matrix product states to efficiently represent ground states for one-dimensional systems with a spectral gap, while certain other one-dimensional problems, without the gap assumption, almost certainly have no efficient way for us to even represent the ground state on a classical computer. I will also discuss recent results on higher-dimensional matrix product states, in an attempt to extend the remarkable success of matrix product algorithms beyond one dimension.

As physicists, we have become accustomed to the idea that a theory\\\'s content is always most transparent when written in coordinate-free language. But sometimes the choice of a good coordinate system is very useful for settling deep conceptual issues. Think of how Eddington-Finkelstein coordinates settled the longstanding question of whether the event horizon of a Schwarzschild black hole corresponds to a real spacetime singularity or not. Similarly we believe for an information-oriented or Bayesian approach to quantum foundations: That one good coordinate system may (eventually!) be worth more than a hundred blue-in-the-face arguments. This talk will motivate and chronicle the search for one such candidate coordinate system---the so-called Symmetric Informationally Complete Measurement---which has caught the attention of a handful of us here at PI and a handful of our visitors.

After almost a century of observations, the ultra-high energy sky has finally displayed an anisotropic distribution. A significant correlation between the arrival directions of ultra-high cosmic rays measured by the Pierre Auger Observatory and the distribution of nearby active galactic nuclei signals the dawn of particle astronomy. These historic results have important implications to both astrophysics and particle physics.

The Universe offers environments with extreme physical conditions that cannot be realized in laboratories on Earth. These environments provide unprecedented tests for extensions of the Standard Model. I will describe three such \"astrophysical laboratories\", which are likely to represent new frontiers in cosmology and astrophysics over the next decade. One provides a novel probe of the initial conditions from inflation and the nature of the dark matter, based on 3D mapping of the distribution of cosmic hydrogen through its resonant 21cm line. The second allows to constrain the metric around supermassive black holes based on direct imaging or the detection of gravitational waves. The third involves the acceleration of high-energy particles in cosmological shock waves. I will describe past and future observations of these environments and some related theoretical work.

This will be an introductory talk about Topological Quantum Computation. TQC is attractive because it is intrinsicaly decoherence free. We introduce the basic notions, such as non abelian anyons, quantum symmetries and topological order. A topologically ordered phase is a gapped phase in which the basic degrees of freedom are of a topological nature (denoted as anyons), charactetized by their fusion and braiding properties. If time permits possible implementations based on Quantum Hall systems will be discussed as well.

Laser cooling and precision spectroscopy provide powerful tools for exploring quantum measurement and metrology using atoms as sensors. In this talk I will discuss our ongoing work to bring together abstract ideas of quantum parameter estimation and concrete physical details of atom-photon interactions in the specific context of magnetometry. I will also present some new ideas on how laser probing of cold atoms could provide a basis for developing entanglement-enhanced spin gyroscopes.

The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Fubini-Study metric. The physical characteristics of a given quantum system can then be represented by a variety of geometrical structures that can be identified in this manifold. This talk will review a number of examples of such structures as they arise in the state spaces of spin-1/2, spin-1, spin-3/2, and spin-2 systems, and various types of entangled systems, all of which have fascinating and beautiful geometries associated with them. The geometric approach offers interesting insights into the nature of quantum systems, and is also useful in the consideration of foundational issues such as those related to the measurement problem.

The role of outflows in global star formation processes has become hotly debated even as fundamental questions about the nature of these outflows continues to receive attention. In this talk I discuss both problems and new approaches to their resolution. Astrophysical outflows have always been a subject at the forefront of the numerical technologies and in the first act of the talk I introduce AstroBEAR, a new Adaptive Mesh Refinement MHD tool developed at Rochester for the study of star formation outflow issues. The question of \'feedback\', the mechanisms by which protostellar outflows can drive turbulence in either clouds or clusters, is then addressed via AstroBEAR simulations. In these studies we seek to understand the detailed mechanisms by which outflows can return energy to their environment and, perhaps, drive turbulent motions. Finally we turn to the MHD processes involved with the outflows themselves and focus on a new tool, High Energy Density Laboratory experiments. I will present results from a campaign of experiments carried out at Imperial Collage in London which directly address issues of magnetically dominated radiative outflows and jets.

One of the cool, frustrating things about quantum theory is how the once-innocuous concept of "measurement" gets really complicated. I'd like to understand how we find out about the universe around us, and how to reconcile (a) everyday experience, (b) experiments on quantum systems, and (c) our theory of quantum measurements. In this talk, I'll try to braid three [apparently] separate research projects into the beginnings of an answer. I'll begin from the premise that you make a measurement to find something out, then attack some specific questions: "How do we find out about quantum systems?", "What can we find out about quantum systems?", and finally "What do we actually know, afterward?" I'll give precise statements of these questions, then present [partial] answers.

Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a classical curved spacetime, as described by general relativity. QFTCS has been applied to describe such important and interesting phenomena as particle creation by black holes and perturbations in the early universe associated with inflation. However, by the mid-1970\'s, it became clear from phenomena such as the Unruh effect that \'particles\' cannot be a fundamental notion in QFTCS. By the mid-1980\'s it was understood how to give a mathematically rigorous formulation of the theory of a free quantum field in curved spacetime. During the past decade, major progress has been made in providing a completely mathematically satisfactory formulation of renormalization in interacting QFTCS, thereby overcoming the difficulties caused by the absence of Poincare symmetry as well as the lack of a preferred vacuum state and a fundamental notion of \'particles\'. This talk will describe these developments and some of the insights that have thereby been attained.

I will discuss an alternative approach to simulating Hamiltonian flows with a quantum computer. A Hamiltonian system is a continuous time dynamical system represented as a flow of points in phase space. An alternative dynamical system, first introduced by Poincare, is defined in terms of an area preserving map. The dynamics is not continuous but discrete and successive dynamical states are labeled by integers rather than a continuous time variable. Discrete unitary maps are naturally adapted to the quantum computing paradigm. Grover's algorithm, for example, is an iterated unitary map. In this talk I will discuss examples of nonlinear dynamical maps which are well adapted to simple ion trap quantum computers, including a transverse field Ising map, a non linear rotor map and a Jahn-Teller map. I will show how a good understanding of the quantum phase transitions and entanglement exhibited in these models can be gained by first describing the classical bifurcation structure of fixed points.