Talks

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and communication.

A full analysis of QCD, the fundamental theory of subnuclear structure and interactions, relies upon numerical simulations and the lattice approximation. After being stalled for almost 30 years, recent breakthroughs in lattice QCD allow us for the first time to analyze the low-energy structure of QCD nonperturbatively with few-percent precision. This talk will present a non-technical overview of the history leading up to these breakthroughs, and survey the wide array of applications that have been enabled by them. It will focus in particular on the impact of these new techniques on experiments that explore such areas as heavy-quark and Standard Model physics.

We discuss the properties of matter in the low temperature regime at density that may exist in the core of compact stars. Assuming that in these conditions quarks are deconfined the attractive color interaction determines the formation of Cooper pairs of quarks and the resulting quark matter has properties analogous to standard superconductors. We show that under reasonable conditions a state were Cooper pairs have non-zero total momentum is energetically favored and the resulting non-homogeneous condensate is characterized by a crystal symmetry. Studying the elastic properties of such a state we find that it behaves like a solid crystal with a very large shear modulus. Our results raise the possibility that (some) pulsar glitches may originate within the Crystalline Color Superconductor core of Neutron stars.

In this talk I describe a possible connection between quantum computing and Zeta functions of finite field equations that is inspired by the \'spectral approach\' to the Riemann conjecture. This time the assumption is that the zeros of such Zeta functions correspond to the eigenvalues of finite dimensional unitary operators of quantum mechanical systems. To model the desired quantum systems I use the notion of universal, efficient quantum computation. Using eigenvalue estimation, such quantum systems should be able to approximately count the number of solutions of the specific finite field equations with an accuracy that does not appear to be feasible classically. For certain equations (Fermat hypersurfaces) one can indeed model their Zeta functions with efficient quantum algorithms, which gives some evidence in favor of the proposal. In the case of equations that define elliptic curves, the corresponding unitary transformation is an SU(2) matrix. Hence for random elliptic curves one expects to see the kind of statistics predicted by random matrix theory. In the last part of the talk I discuss to which degree this expectation does indeed hold. Reference: arXiv:quant-ph/0405081

During multi-field Inflation, the curvature perturbation can evovlve on superhorizon scales and will develop non-gaussianity due to non-linear interactions. In this talk I will discuss the calculation of this effect for models of inflation with two scalar fields.