Since 2002 Perimeter Institute has been recording seminars, conference talks, public outreach events such as talks from top scientists 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 and 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.
Accessibly by anyone with internet, Perimeter aims to share the power and wonder of science with this free library.
I will report on an ongoing project to work out and exploit an analogue of Schur-Weyl duality for the Clifford group. Schur-Weyl establishes a one-one correspondence between irreps of the unitary group and those of the symmetric group. A similar program can be carried out for Cliffords.
The permutations are then replaced by certain discrete orthogonal maps.
Affleck, Kennedy, Lieb, and Tasaki (AKLT) constructed one-dimensional and two-dimensional spin models invariant under spin rotation. These are recognized as paradigmatic examples of symmetry-protected topological phases, including the spin-1 AKLT chain with a provable nonzero spectral gap that strongly supports Haldane’s conjecture on the spectral gap of integer chains.
The manipulation of quantum "resources" such as entanglement and coherence lies at the heart of quantum advantages and technologies. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are inevitably contaminated by noises and thus often lost their power or become unreliable for direct usage. Here we derive fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource.
Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
With the detection of GW170817 we have observed the first multi messenger signal from two merging neutron stars. This signal carried a multitude of information about the underlying equation of state (EOS) of nuclear matter, which so far is not known for densities above nuclear saturation. In particular it is not known if exotic states or even a phase transition to quark matter can occur at densities so extreme that they can't be probed by any current experiment.
There is a standard generalization of stabilizer codes to work with qudits which have prime dimension, and a slightly less standard generalization for qudits whose dimension is a prime power. However, for prime power dimensions, the usual generalization effectively treats the qudit as multiple prime-dimensional qudits instead of one larger object. There is a finite field GF(q) with size equal to any prime power, and it makes sense to label the qudit basis states with elements of the finite field, but the usual stabilizer codes do not make use of the structure of the finite field.
A self-correcting quantum memory can store and protect quantum information for a time that increases without bound in the system size, without the need for active error correction. Unfortunately, the landscape of Hamiltonians based on stabilizer (subspace) codes is heavily constrained by numerous no-go results and it is not known if they can exist in three dimensions or less. In this talk, we will discuss the role of symmetry in self-correcting memories.