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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.

We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB supergravity dual to N=(0,2) SCFTs in d=2, as well as  $AdS_2\times Y_9$ solutions of D=11 supergravity dual to N=2 supersymmetric quantum mechanics, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. The relevant geometry on $Y_{2n+1}$, $n\ge 3$ was first identified in 2005-2007 and around that time infinite classes of explicit examples solutions were also found but, surprisingly, there was little progress in identifying the dual SCFTs. We present new results which change the status quo. For the case of $Y_7$, a variational principle allows one to calculate the central charge of the dual SCFT without knowing the explicit metric. This provides a geometric dual of c-extremization for d=2 N=(0,2) SCFTs analogous to the well known geometric duals of a-maximization of d=4 N=1 SCFTs and F-extremization of d=3 N=2 SCFTs in the context of Sasaki-Einstein geometry.  In the case of $Y_9$ a similar variational principle can be used to obtain properties of the dual N=2 quantum mechanics as well as the entropy of a class of supersymmetric black holes in $AdS_4$ thus providing a geometric dual of $I$-extremization.

Understanding entanglement in QFTs is a challenging topic that involves many aspects. One important probe for this is the modular (or entanglement) Hamiltonian, which is closely related to the Unruh effect. We determine this operator for the chiral fermion at finite temperature on the circle using complex analysis, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits. We also derive the first exact results for the entanglement and relative entropies of this system for the different spin sectors. Based on [1905.05768,1906.02207].

In this talk I will report on recent progress in building QFT models on causal sets. The framework I'm using is that of perturbative algebraic quantum field theory (pAQFT). It was developed for rigorous study of perturbative QFT in the continuum, but can also be applied in the situation where spacetime is replaced by a discrete structure. Causality plays a key role in pAQFT, so it is natural to apply it to causets. Construction of models in this framework is purely algebraic and one does not need to specify a state or a Hilbert space representation until the final step, in which correlation functions are computed.

 In the 90s Turaev, Viro, Barrett and Westbury constructed a (2+1)D state sum TQFT associated to any fusion category. The associated phases of matter were popularized by Kiteav, Levin and Wen and are now central  examples in condensed matter physics and quantum information theory.

Despite the importance of these phases, many of the computational techniques for working with fusion categories have not percolated into condensed matter physics. Many of these techniques are "folk theorems"
and have not appeared in the literature in a digestible form.

Jacob Bridgeman and myself have spent the last two years extracting these computational techniques from Corey Jones, and have been using them to understand defects in Levin-Wen phases. Our papers 1806.01279,
1810.09469, 1901.08069, 1907.06692 document the development of our understanding, and demonstrate how to do physically relevant fusion category computations.