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.
Clifford group as symplectic group, generators of the Clifford group & encoding circuits for stabilizer codes, efficient simulation of Clifford group circuits, efficient simulation of Pauli measurements
We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $beta=0$ the BPS-saturated domain wall interpolating between
them has a moduli space parameterized by a U(1) phase $sigma$ which can
be promoted to a scalar field in the effective low-energy theory on the
wall world-volume. At small nonvanishing $beta$ this field gets a
sine-Gordon potential. As a result, only two discrete degenerate BPS
If a large quantum computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a conventional computer? In this talk, I argue that a QC could solve some relevant physical "questions" more efficiently. First, I will focus on the quantum simulation of quantum systems satisfying different particle statistics (e.g., anyons), using a QC made of two-level physical systems or qubits.
The mathematical formalism of quantum theory has many features whose physical origin remains obscure. In this paper, we attempt to systematically investigate the possibility that the concept of information may play a key role in understanding some of these features. We formulate a set of assumptions, based on generalizations of experimental facts that are representative of quantum phenomena and physically comprehensible theoretical ideas and principles, and show that it is possible to deduce the finite-dimensional quantum formalism from these assumptions.
Universal Enveloping Algebras and dual Algebras of Functions
The two most relevant types of Hopf-algebras for applications in physics are discussed in this unit. Most central notion will be their duality and representation.
Hopf-Algebras and their Representations
In order to consolidate the above motivation, we have to introduce Hopf-algebras on a mathematical footing. We define Hopf-algebras, discuss duality and especially we will have a closer look at the question why coproducts induce a multiplication on the dual algebra but not the other why around. With these preparations we close this unit by the discussion of representations and corepresentations - and how these are related for dual Hopf-algebras.
Motivation: From Quantum Mechanics to Quantum Groups
The notion of 'quantization' commonly used in textbooks of quantum mechanics has to be specified in order to turn it into a defined mathematical operation. We discuss that on the trails of Weyl's phase space deformation, i.e. we introduce the Weyl-Moyal starproduct and the deformation of Poisson-manifolds.
Generalizing from this, we understand, why Hopf-algebras are the most genuine way to apply 'quantization'
to various other algebraic objects - and why this has direct physical applications.
If spacetime is "quantized" (discrete), then any equation of motion compatible with the Lorentz transformations is necessarily non-local. I will present evidence that this sort of nonlocality survives on length scales much greater than Planckian, yielding for example a nonlocal effective wave-equation for a scalar field propagating on an underlying causal set. Nonlocality of our effective field theories may thus provide a characteristic signature of quantum gravity.