Talks

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

I will talk about the generalization of Berry classes for quantum lattice spin systems. It defines invariants of topologically ordered states or families thereof. In particular, its equivariant version for 2d gapped states gives the zero-temperature Hall conductance and its various generalizations. I will also discuss the construction of chiral states realizing the topological order associated with a unitary rational vertex operator algebra for which these invariants are non-trivial

Zoom link:  https://pitp.zoom.us/j/99910103969?pwd=VlVHVGRiV29iVEFyTXZyR3ovMkRaQT09

The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum mechanical wavefunction of the universe. In this talk I will discuss how we can adapt flat space bootstrapping techniques to the quantum fluctuations in the early universe, in particular showing that the requirement of unitary time evolution, colloquially the conservation of probabilities, fixes the analytic structure of the wavefunction and of all the cosmological correlators it encodes.

Zoom link:  https://pitp.zoom.us/j/95812107239?pwd=bVZMcWdHTVM0Y0tFZGMxS2FCVGF0Zz09

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09

A well-established approach to solving interacting quantum systems is variational Monte Carlo. There is a lot of renewed interest in it since the introduction of neural networks as a highly expressive and unbiased variational ansatz. Similar to more traditional ansätze, neural networks struggle with solving frustrated quantum systems. A conjecture has been made that the cause of these difficulties lies in the sign structures of the ground state wavefunctions. Here, we will discuss these sign structures in more detail and try to analyze how complex they really are by establishing a connection to classical Ising models.

Zoom link:  https://pitp.zoom.us/j/99087954160?pwd=Vm5zWWRFbHBwVFR1RHZMc3ptem03QT09