Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres. Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities. Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA). PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org.
Transversality is one of the most desirable features of fault-tolerant circuits because it automatically limits the propagation of errors. However, it was shown by Eastin & Knill that no universal set of quantum gates on any quantum code is transversal. In this talk, we strengthen this result for stabilizer codes to say that transversal gates must in fact be contained in the Clifford hierarchy. Moreover, we present new circuits on Bacon-Shor codes that saturate our bounds.
I will explain a general strategy to lift (2+1)D topological phases, in particular string nets, to (3+1)D models with line defects. This allows a systematic construction of (3+1)D topological theories with defects, including an improved version of the Walker-Wang Model. It has also an interesting application to quantum gravity as it leads to quantum geometry realizations for which all geometric operators have discrete and bounded spectra. I will furthermore comment on some interesting (self-) duality relations that emerge in these constructions.
Ground state degeneracy is an important characteristic of topological order. It is a natural question under what conditions such topological degeneracy extends to higher energy states or even to the full energy spectrum of a model, in such a way that the degeneracy is preserved when the Hamiltonian of the system is perturbed. It appears that Ising/Majorana wires have this property due to the presence of robust edge zero modes.
It is well known that commutative Frobenius algebras can be represented as topological surfaces, using the graphical calculus of dualizable objects in monoidal 2-categories. We build on related ideas to show that the interacting Frobenius algebras of Duncan and Dunne, which have a Hopf algebra structure, arise naturally in a similar way, by requiring a single 3-morphism in a 3-category to be invertible.
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For a manifold with boundary, the tensor network has free indices that can be associated to qudits, and its contraction gives the coefficients of a quantum error-correcting code. The code has local stabilizers determined by Levin and Wen.
The unrenormalised energy momentum tensor is both huge and fluctuating from point to point. Taking this seriously we (Qingdi Wang, Zhen Zhu, and myself) argue that the slow exponential expansion of the universe (on time scales of 10^10 years) comes from a very weak parametric resonance induced by the fluctuating energy mementum tensor on the rapidly fluctuating scale factor (on time scales much shorter than the Planck scale). We see only the slow exponential growth because we avarage over the scale factor squared.
The quantum double models are parametrized by a finite-dimensional semisimple Hopf algebra (over $\mathbb{C}$). I will introduce the graphical calculus of these Hopf algebras and sketch how it is equivalent to the calculus of two interacting symmetric Frobenius algebras. Since symmetric Frobenius algebras are extended 2D TQFTs, this suggests that there is a canonical way to 'lift' a compatible pair of 2D TQFTs to a 3D TQFT.