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PERIMETER INSTITUTE RECORDED SEMINAR ARCHIVE

PIRSA:C08009 - Quantum Information and Graph Theory: Emerging Connections - 2008PODCAST Subscribe to podcast

Quantum Information and Graph Theory: Emerging Connections

Organizer(s): Robert Raussendorf   Peter Hoyer   Michele Mosca   David Feder   Simone Severini  

Collection URL: http://pirsa.org/C08009

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Complex Lines
Speaker(s): Chris Godsil
Abstract: Certain structures arising in Physics (mub's and sic-povm's) can be viewed as sets of lines in complex space that are as large as possible, given some simple constraints on the angles between distinct lines. The analogous problems in real space have long been of interest in Combinatorics, because of... read more
Date: 28/04/2008 - 9:50 am

Pseudo-random quantum states and operations
Speaker(s): Aram Harrow
Abstract: The idea of pseudo-randomness is to use little or no randomness to simulate a random object such as a random number, permutation, graph, quantum state, etc... The simulation should then have some superficial resemblance to a truly random object; for example, the first few moments of a random variabl... read more
Date: 28/04/2008 - 11:10 am

Quantum information, graphs, and statistical mechanics
Abstract: We give an overview of several connections between topics in quantum information theory, graph theory, and statistical mechanics. The central concepts are mappings from statistical mechanical models defined on graphs, to entangled states of multi-party quantum systems. We present a selection of such... read more
Date: 28/04/2008 - 2:00 pm

Matchgates and the classical simulation of associated quantum circuits
Speaker(s): Richard Jozsa
Abstract: Some years ago Valiant introduced a notion of 'matchgate' and 'holographic algorithm', based on properties of counting perfect matchings in graphs. This provided some new poly-time classical algorithms and embedded in this formalism, he recognised a remarkable class of quantum circuits (arising when... read more
Date: 28/04/2008 - 2:50 pm

A unifying view of graph theory in quantum field theory
Speaker(s): Achim Kempf
Abstract: A fundamental theorem of quantum field theory states that the generating functionals of connected graphs and one-particle irreducible graphs are related by Legendre transformation. An equivalent statement is that the tree level Feynman graphs yield the solution to the classical equations of motion. ... read more
Date: 28/04/2008 - 4:00 pm

Statistical Mechanical Models and Topological Color Codes.
Speaker(s): Hector Bombin
Abstract: We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack lattices. This mapping allows us to test that different comp... read more
Date: 29/04/2008 - 2:50 am

On the Pauli graphs of N-qudits
Speaker(s): Michel Planat
Abstract: A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N-qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and ... read more
Date: 29/04/2008 - 9:50 am

Yang-Baxter Equations, Extra-special Two-groups and Topological-like Features in Quantum Information Theory
Speaker(s): Yong-Shi Wu
Abstract: 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 ... read more
Date: 29/04/2008 - 11:10 am

Is there a classical analogue of measurement-based quantum computation?
Speaker(s): Dan Browne
Abstract: 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 measu... read more
Date: 29/04/2008 - 2:00 pm

Exotic Phases and Entanglement Properties of Condensed Matter Systems Living on Graphs
Speaker(s): Pasquale Sodano
Abstract: 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 ... read more
Date: 29/04/2008 - 4:00 pm

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