NB: non-standard time!

Title: Symmetry-weighted ensemble averaging from TQFT gravity

Abstract: In a recently proposed framework of TQFT gravity (2310.13044, 2405.20366) -- a toy model of AdS3 gravity -- a bulk 3d TQFT summed over all topologies is shown to be dual to a unitary ensemble of boundary 2d CFTs. I will show that the CFTs in this ensemble are weighted by the inverse of the order of their symmetry group (relative to the categorical symmetry provided by the bulk TQFT as a SymTFT). Mathematically, this is the natural measure over the groupoid of the TQFT Lagrangian algebras that construct the CFTs, and the holographic duality then provides a generalization of the Siegel-Weil formula beyond averaging over bosonic lattice-CFTs. I will also discuss some examples for rational CFTs as well as implications to noncompact TQFTs and pure gravity.

Most objects around us are in thermal equilibrium. But are some
systems "more thermal" than others?
The emerging paradigm of deep thermalization and projected ensembles
has indeed demonstrated that there can be
different degrees of thermality, depending on how much information can
be extracted from the system and, relatedly,
the behavior of multiple copies of the system. In my talk I will discuss a
related concept of observable projected ensembles and a
field-theoretic approach to this problem based on the replica trick.
Bases on https://arxiv.org/abs/2410.21397 and on-going work.

I will describe the dynamical evolution of a universe containing a single black hole. If the black hole has sufficiently large initial charge, it will be driven very close to extremality by the emission of neutral Hawking radiation, while charged particle emission is exponentially suppressed. At low enough temperatures, quantum gravity becomes important and Hawking-style quantum field theory in curved spacetime calculations give completely incorrect answers, even for simply questions like the energy spectrum of emitted radiation. This leads to interesting new physics, e.g. in certain regimes the dominant radiation channel becomes entangled pairs of photons, as in the “forbidden’’ 2s->1s hydrogen atom transition. By careful analysis of the relevant metric fluctuations, we can calculate the quantum gravity effects in a controlled manner and tell the complete story of the black hole evaporation in both a universe with a matter content similar to ours as well as in a supersymmetric universe.

All (Poincaré + gauge)-symmetry-preserving lattice theories can be constructed using a discrete derivative and its inverse (lattice integral) that seem to satisfy the same calculi of the continuum. In this sense the discrete operations are exact for which there are certain preliminary evidences. Noting that the mathematical tool needed to construct a classical field theory in the continuum is that of the Schwartz class functions and tempered distributions, we embark on attacking the full-fledged problem at hand, i.e. to develop the tempered distribution theory on the lattice. Some of the key results our construction leads to are as follows: (1) Exact operations satisfy exactly the same calculi of the continuum. Kronecker delta satisfies the same continuum distributional identities of the Dirac delta on the lattice with respect to the exact derivative. This allows one to prove Noether's theorems and derive symmetry algebras for the lattice theories. (2) Lattice configuration space (Schwartz space) corresponds to a subspace of the continuum configuration space that carries lattice cutoff as a parameter such that: (A) Lattice path integral is same as the continuum path integral over this subspace. By construction, the latter is UV divergence free. This must be true non-perturbatively. (B) The subspace is closed under Poincaré and gauge transformations. This is the root cause for the symmetries being preserved on the lattice. (C) Preliminary observations indicate that this may be a dense subspace.

Quantum Error Correction (QEC) is essential for protecting fragile quantum states against physical noise, a prerequisite for reliable quantum computation. A key component of QEC is syndrome decoding—determining which recovery operation to apply using measured error syndromes. While decoding linear classical codes is NP-complete, the quantum version is #P-complete, presenting an even greater challenge. Achieving practical solutions is therefore critical to unlock the exponential advantages promised by quantum computing.

In this talk, we introduce a new formulation of syndrome decoding for quantum stabilizer codes as a Quadratic Unconstrained Binary Optimization (QUBO) problem. By leveraging well-established QUBO algorithms, this approach allows tuning the trade-off between solution accuracy and algorithm runtime. Preliminary numerical results for various quantum low-density parity-check (qLDPC) codes show robust decoding performance and the emergence of a code-capacity threshold with polynomial runtime.

Zoom Link: https://uky.zoom.us/j/82369158320?pwd=N9RVyw0Gn2g85GKc6ZmSjnSxnz2pjc.1