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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.

Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor of spin liquid states on the kagome lattice. As their ground state, spin-1 excited states for spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). We find that DSL has no explicit contradiction with experiments. Besides a fractionalized spin moment, DSL has a fractionalized crystal momentum which is also detectable directly in the neutron scattering measurements.

We study non-Fermi liquids that arise at the quantum critical points associated with the spin and charge density wave transitions in metals with the C2 symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in 3 − epsilon dimensional momentum space. In three dimensions, marginal Fermi liquids arise at the spin and charge density wave critical points. Below three dimensions, a perturbative anisotropic non-Fermi liquid is realized at the spin density wave critical point, where not only time but also different spatial coordinates develop distinct anomalous dimensions. On the other hand, the perturbative expansion breaks down at the charge density wave critical point immediately below three dimensions.

Motivated by results of DMRG and tensor network simulations on doped $t$-$J$ model on honeycomb lattice, we study superconductivity of singlet and triplet pairing in this model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half-filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a non-trivial state with Chern number two.

We studied t1-t2-J1-J2 model on Honeycomb lattice at finite doping. We find that when t_1 is very small, the t1-t2-J1-J2 model on Honeycomb lattice may be in a supperconducting phase. Such a supperconducting phase is not driven by the pairing, but by entanglement.