Talks

There is a growing list of examples where soft factorization theorems in scattering amplitudes can be understood as Ward identities of asymptotic charges. I will review some of these, with emphasis on cases that are not associated to usual conservation laws: leading scalar, subleading photon and sub-subleading graviton soft theorems.

The surface code is currently the leading proposal to achieve fault-tolerant quantum computation. Among its strengths are the plethora of known ways in which fault-tolerant Clifford operations can be performed, namely, by deforming the topology of the surface, by the fusion and splitting of codes, and even by braiding engineered Majorana modes using twist defects. Here, we present a unified framework to describe these methods, which can be used to better compare different schemes and to facilitate the design of hybrid schemes. Our unification includes the identification of twist defects with the corners of the planar code. This identification enables us to perform single-qubit Clifford gates by exchanging the corners of the planar code via code deformation. We analyze ways in which different schemes can be combined and propose a new logical encoding. We also show how all of the Clifford gates can be implemented with the planar code, without loss of distance, using code deformations, thus offering an attractive alternative to ancilla-mediated schemes to complete the Clifford group with lattice surgery.

I will give an overview of the causal set approach to quantum gravity, and what makes this "fork in the road" distinct from other approaches.  Motivated by deep theorems in Lorentzian geometry, causal set theory (CST) posits that the underlying fabric of spacetime is  atomistic and encoded in a locally finite partially ordered set. In  the continuum  approximation,  the partial order corresponds to the causal structure, and the cardinality to the conformal factor.  Together, these give the approximate continuum geometry.  Lorentz invariance emerges as a consequence, but brings with it a certain  "non-locality”, which distinguishes CST  from other approaches in an essential way. It also makes the  reconstruction of spacetime geometry from the causal set particularly challenging.  I will describe some of the progress we have made in this geometric reconstruction program. I will then describe a particular formulation of CST dynamics inspired by the continuum path integral and discuss what we have learnt so far and where it is taking us. 

The path integral formulation of quantum mechanics has been immensely influential, particularly in high energy physics. However, its applications to quantum circuits has so far been more limited. In this talk I will discuss the sum-over-paths approach to computing transition amplitudes in Clifford circuits. In such a formulation, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action which is provided by the discrete Wigner representation. As an application of the sum-over-paths technique I will show how to recover a version of the Gottesman-Knill theorem, namely that the transition amplitudes in Clifford circuits can be computed efficiently.

I discuss some aspects of boundary conformal field theories (bCFTs). I will demonstrate that free bCFTs have a universal way of satisfying crossing symmetry constraints. I will introduce a simple class of interacting bCFTs where the interaction is restricted to the boundary. Finally, I will discuss relationships between boundary trace anomalies and boundary limits of stress-tensor correlation functions.