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We show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. Negativity in a quasiprobability function is not required, neither in states nor the operations. Our result is consistent with Gleason’s Theorem and the PBR theorem. This is joint work with Michael Zurel and Cihan Okay; see arXiv:2004.01992.

Zoom: https://harvard.zoom.us/j/779283357

\hat{Z} is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients), which has interesting modular properties. While originally from physics, this invariant has been mathematically constructed for a big class of 3-manifolds, and conjecturally it can be extended to all 3-manifolds. In this talk, I will give a gentle introduction to \hat{Z} and what is known about it, as well as highlighting some recent developments, including the use of R-matrix, generalization to higher rank, large N-limit and interpretation as open topological string partition functions.

Zoom: https://harvard.zoom.us/j/94717938264