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.
We will review the topic of tensor network renormalization, relate it to real space Hamiltonian flows, and discuss the emergence of matrix product operator algebras as symmetries of the renormalization fixed points.
joint work with Matthias Bal, Michael Marien and Jutho Haegeman
I will discuss analytic approaches to construct tensor network representations of quantum field theories, more specifically conformal field theories in 1+1 dimensions. A key insight is that we should understand how well the tensor network can reproduce the correlation functions of the quantum field theory. Based on this measure of closeness, I will present rigorous results allowing for explicit error bounds which show that both Matrix product states (MPS) as well as the multiscale renormalization Ansatz (MERA) do approximate conformal field theories.
We normally think of large accelerators and large-scale cosmic events when we consider the frontiers of elementary particle physics, pushing to understand the universe at higher and higher energy scales. However, several tabletop low-energy experiments are posed to discover a wide range of new physics beyond the Standard model, where feeble interactions require precision measurements rather than high energies. In our experiments, high-Q resonant sensors enable ultra-sensitive force and field detection.
Tensor networks have primarily, thought not exclusively, been used to the describe quantum states of lattice models where there is some inherent discreteness in the system. This raises issues when trying to describe quantum field theories using tensor networks, since the field theory is continuous (or at least the regulator should not play a central role). I'll present some work in progress studying tensor networks designed to directly compute correlation functions instead of the full state.
We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).
The exact renormalization group (ERG) for O(N) vector models at large N on flat Euclidean space admits an interpretation as the bulk dynamics of a holographically dual higher spin gauge theory on AdS_{d+1}. The generating functional of correlation functions of single trace operators is reproduced by the on-shell action of this bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. This structure arises because of an enormous non-local symmetry of free fixed point theories.
The first half of the talk will introduce the cMERA, as proposed by Haegeman, Osborne, Verschelde and Verstratete in 2011 [1], as an extension to quantum field theories (QFTs) in the continuum of the MERA tensor network for lattice systems. The second half of the talk will review recent results [2] that show how a cMERA optimized to approximate the ground state of a conformal field theory (CFT) retains all of its spacetime symmetries, although these symmetries are realized quasi-locally.