Talks

Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively studied in band theory and have been experimentally discovered, the classification and diagnosis of their strongly interacting counterparts are relatively less well understood. Here we present a unified scheme for constructing all topological crystalline states, bosonic and fermionic, free and interacting, from real-space "building blocks" and "connectors". Building blocks are finite-size pieces of lower dimensional topological states protected by onsite symmetries alone, and connectors are "glue" that complete the open edges shared by two or multiple pieces of building blocks. The resulted assemblies are selected against two physical criteria we call the "no-open-edge condition" and the "bubble equivalence", which, respectively, ensure that each selected assembly is gapped in the bulk and cannot be deformed to a product state. The scheme is then applied to obtaining the full classification of bosonic topological crystalline states protected by several onsite symmetry groups and each of the 17 wallpaper groups in two dimensions and 230 space groups in three dimensions. We claim that our real-space recipes give the complete set of topological crystalline states for bosons and fermions, and prove the boson case analytically using a spectral sequence expansion of group cohomology.

The no-signalling principle, preventing superluminal communication and the consequent logical paradoxes, is typically formulated within the information-theoretic framework in terms of admissible correlations in composite systems. In my talk, I will present its complementary incarnation associated with dynamics of single systems subject to invasive measurements. The `dynamical no-signalling principle' applies to any theory with well defined rules of calculating detection statistics in spacetime. It thus offers a new framework, based on measure theory, for studying ``post-quantum'' theories in spacetime. I will show that, strikingly, the `dynamical no-signalling' principle rules out some of the well know models of quantum wave dynamics.

If General Relativity emerges from quantum gravity, then general covariance, the gauge invariance of GR, will emerge with it. We can ask, within any approach to the problem of quantum gravity, what is the “precursor” principle or precept that will give rise to — or manifest itself as — general covariance in the large scale semi-classical approximation?
Given how important the understanding of general covariance (or lack of it!) was in the development of GR we might expect that thinking about this question will be similarly important in the development of quantum gravity.
I will explain how general covariance is seen from the perspective of the causal set approach to quantum gravity and describe recent progress in creating a framework for causal set dynamics that is completely covariant and does not refer to any gauge degrees of freedom at all.

In quantum error correcting codes, there is a distinction
between coherent and incoherent noise. Coherent noise can cause the
average infidelity to accumulate quadratically when a fixed channel is
applied many times in succession, rather than linearly as in the case
of incoherent noise. I will present a proof that unitary single qubit
noise in the 2D toric code with minimum weight decoding is mapped to
less coherent logical noise, and as the code size grows, the coherence
of the logical noise channel is suppressed. In the process, I will
describe how to characterize the coherence of noise using either the
growth of infidelity or the relation between the diamond distance from
identity and the average infidelity. I will explain how coherence in
the noise on physical qubits is transformed by error correction in
stabilizer codes. Then, I will sketch the proof that coherence is
suppressed for the 2D toric code. The result holds even when the
single qubit unitary rotation are allowed to have arbitrary directions
and angles, so long as the angles are below a threshold, and even when
the rotations are correlated. Joint work with John Preskill.