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.
It is well-known that if a graph G_1 can be obtained from another graph G_2 by removing a degree-2 vertex and combing its two neighbors, the graph state |G_1> can be obtained from |G_2> through LOCC. In this talk, I will describe how to construct a graph G\' from a given graph G so that (a) The maximum degree of G\', Delta(G\'), is no more than 3. (b) G can be obtained from G\' by a sequence of contraction operations described above. (c) The treewidth of G\', tw(G\'), is no more than tw(G)+1. (d) The construction takes exp(O(tw(G))) time.
It is well known that the toric code model supports abelian anyons. It can be realized on a square lattice of qubits, where the anyons are represented by the endpoints of strings of Pauli operators. We will demonstrate that the non-abelian Ising model can be realized in a similar way, where now the string operators are elements of the Clifford group. The Ising anyons are shown to be essentially superpositions of the abelian toric code ones, reproducing the required fusion, braiding and statistical properties.
One of the main strengths of the ERG is that it admits nonperturbative approximation schemes which preserve renormalizability. I will introduce a particularly powerful scheme, the derivative expansion.
This talk will report recent work on two themes that relate concepts in graph theory to problems in quantum information theory. We will discuss the quantum analogue of expander graphs which prove to be of key importance when de-randomizing algorithms in classical computer science. Using powerful ideas of discrete phase space methods, efficiently implementable quantum expanders can be constructed based on an argument that barely fills three lines.
I will discuss a quantum algorithm for the exact evaluation of the classical Potts partition function for a class of graphs (and hypergraphs) related to a family of classical cyclic codes. I will also present a mapping I recently constructed from quantum circuit instances to graphs and discuss some relationships to the classical Ising partition function.
Consider the quantum predictions for EPR-type measurements on two systems with Hilbert space of dimension at least 3 in any maximally entangled state. I show that the only possible hidden variables model of these probabilities that satisfies both Shimony\'s and Jarrett\'s condition of parameter independence (or `locality\') and Jones and Clifton\'s condition of conditional parameter independence (or `constrained locality\') is trivial, i.e. given by the quantum probabilities themselves. I shall attempt to discuss also the meaning of the conditions and of this result.
New and exotic phases as well as remarkable entanglement behaviors emerge in condensed matter systems (and quantum devices) living (fabricated) on graphs. To illustrate this, I will discuss the properties of Josephson junction networks fabricated on comb and star graphs and of spin models living on pertinent fiber-graphs.
Measurement-based quantum computation is unusual among quantum computational models in that it does not have an obvious classical analogue. In this talk, I shall describe some new results which shed some new light on this. In the one-way model [1], computation proceeds by adaptive single-qubit measurements on a multi-qubit entangled \'cluster state\'. The adaptive measurements require a classical computer, which processes the previous measurement outcomes to determine the correct bases for the following measurement.
Many string theorists and cosmologists have recently turned their attention to building and testing string theory models of inflation. One of the main goals is to find novel features that could distinguish stringy models from their field theoretic counterparts. This is difficult because, in most examples, string theory is used to derived an effective theory operating at energies well below the string scale.
Recently a simple but perhaps profound connection has been observed between the unitary solutions of the Yang-Baxter Equations (YBE) and the entangled Bell states and their higher dimensional (or more-qubit) extensions, the generalized GHZ states. We have shown that this connection can be made more explicit by exploring the relation between the solutions of the YBE and the representations of the extra-special two-groups.