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The last decade has seen the impressive development of quantum information science, both in theory and in experiment. There are many measures that can be used to assess the achievements in the field: new algorithms, new applications and larger quantum processors, to name a few. The discovery of quantum algorithms has demonstrated the potential power of quantum information. As pointed out by Bill some years ago, to realize this potential requires the ability to overcome the imprecision and imperfection inherent in physical systems. Quantum error correction (QEC) has provided a solution, showing that errors can be corrected with a reasonable amount of resources as long as their rate is sufficiently small. Implementing QEC protocols remains one of the most important challenges in QIP. In the experimental arena, the quest to build quantum processors that could outperform their classical counterparts has led to many blueprint proposals for potential devices based on NMR, electron spin resonance, ion traps, atom traps, optics, superconducting devices and nitrogen-vacancy centres, among others. Many have demonstrated not only the possibility of controlling quantum bits, but also the ability to do so in practice, showing the progression of quantum information science from the blackboard to the laboratory. My presentation will give an overview of some of the recent results in quantum information science on the way to implement quantum error correction. I will show how noise can be characterise efficiently when our goal is to find suitable quantum error correcting codes. I will show demonstrations of control to implement some quantum error correcting codes and finally how can noise be extracted through algorithmic cooling. I will comments on some challenges that need to be solved and a path towards implementing many round of quantum error correction.

I review the contentious question, "Does a uniformly accelerated detector radiate?" As Audretsch and Muller pointed out long ago, this is partly a semantic dispute. The talk draws on recent discussions with Alex Calogeracos and George Matsas.

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions.

Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop.

Presented is a discussion of quantum field theory on curved spacetime and of microlocal analysis, with an emphasis on the way that these two areas connected for me personally through a specific problem, namely that of resolving Kay's singularity conjecture for two point functions of a linear scalar field on a globally hyperbolic spacetime. A particular case of this conjecture is presented, namely the translation invariant case on flat Minkowski spacetime, which does not require microlocal analysis. Next, the results of Duistermaat and Hoermander concerning distinguished parametrices of the Klein Gordon equation on a curved spacetime are described, since they lead to the notion of a wave front set (or microlocal) spectral condition, which could be viewed as a remnant of the spectral condition on flat spacetime. This condition on the wavefront set of the two point function has been employed by Brunetti, Koehler and Fredenhagen to develop a method of renormalization on a general curved spacetime, which has been developed further by Hollands and Wald. Other QFT-related topics to which microlocal methods may apply are: Lorentz symmetry breaking models and many body QM models (e.g., the free electron gas in a metal). In the case of vector or spinor models, the polarization set may be used to refine information about the singularities. Similarly, the principal symbol of the two point function, viewed as a Fourier integral operator, is a constant times a canonical half density on the natural Lagrangian submanifold associated with the Klein-Gordon operator, suggesting a tangent space Lorentz invariance property for the free model.

After the completion of the Planck satellite, the next most important experiments in cosmology will be about mapping the Large Scale Structures of the Universe. In order to continue to make progress in our understanding of the early universe, it is essential to develop a precise understanding of this system. The Effective Filed Theory of Large Scale Structures provides a novel framework to analytically compute the clustering of the Large Scale Structures in the weakly non-linear regime in a consistent and reliable way. The theory that describes the long wavelength fluctuations is obtained after integrating out the strongly-coupled, short-distance modes, and adding suitable operators that allow us to correctly reconstruct the effect of short distance fluctuations at long distances. By using techniques that originate in the particle physics context, a few observables have been computed so far, and the results are extremely promising. I will discuss the formalism, the main results so far, and the potential implications for next generation experiments.

The spin-flip transition in neutral hydrogen may be used to probe large-scale structure at high redshifts, before the first luminous objects formed. The huge number of modes potentially accessible make this a very promising avenue. I will discuss several key unknowns that could be measured with high-redshift 21cm surveys: primordial non-gaussianity, the primordial small-scale power spectrum, and dark-matter-baryon interactions. I will close by discussing CMB spectral distortions, another promising probe of early Universe physics, and illustrate how they can be used to test dark-matter interactions with standard model particles.