In Spring 2010, if not explicitely stated otherwise, the seminar takes place Fridays 11AM in Hennings 309B.
Feb 1, 2010 (Theory Seminar): David Feder (U Calgary), Measurement-based quantum computing in a fermionic ground state
Time and Location: Monday, Feb 1, 12 noon, Hennings 318/ coffee and sandwiches
Abstract: Quantum computers have the potential to solve various problems more efficiently than any conceivable classical computer, but building such a device is a major challenge. The main problem is that one needs to have precise control of the components, while otherwise keeping them as isolated as possible from the rest of the environment. Ideally then, a quantum computer would be closely related to the gapped ground state of some natural quantum system, with manipulations on it (such as local rotations and measurements) preserving this central characteristic. Finding candidate Hamiltonians has been difficult, however. It turns out that the vast majority of quantum mechanical states are not useful for quantum information processing in such a model. Even worse, no one even knows what are the important properties that make a state useful or not!
I will discuss the fundamental properties of fermions, and show that under very specific circumstances the gapped ground state of these indistinguishable particles can in fact constitute a universal resource for quantum computation. In this model the quantum information itself becomes fundamentally non-local. Entanglement is associated with fermionic antisymmetry, but alone cannot be used to perform tasks such as quantum teleportation; for this one also needs local particle interactions.
January 27, 2010: Poya Haghnegahdar (UBC), Review of Graphical Quantum Error-Correcting Codes by S. Yu, Q. Chen, and C. H. Oh, arXiv:0709.1780
Time and Location: Friday, Jan 27, 11am, Hennings 309B
Abstract: We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum error correcting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes, which are potentially more efficient, is not as well understood as that of stabilizer codes. Our graphical approach provides a unified and classical way to construct both stabilizer and nonadditive codes. In particular we have explicitly constructed the optimal ((10,24,3)) code and a family of 1-error detecting nonadditive codes with the highest encoding rate so far. In the case of stabilizer codes a thorough search becomes tangible and we have classified all the extremal stabilizer codes up to 8 qubits.
January 20, 2010: Len Goff (UBC), Generalized entanglement
Time and Location: Friday, Jan 20, 11am, Hennings 309B
Abstract: In this talk I will discuss the idea of "generalized entanglement", which is a research program aimed at extending the notion of entanglement beyond a subsystem based decomposition of Hilbert space. Mainly, I will provide an introduction to the idea based on the two references listed below. I will also discuss the motivation for this approach, and we will check that generalized entanglement contains the Schmidt rank measure of conventional entanglement as a special case. Time permitting, I will discuss the prospect of applying generalized entanglement to systems of non-interacting fermions.
L. Viola, H. Barnum, E. Knill, G. Ortiz, R. Somma, Entanglement Beyond Subsystems; arxiv: quant-ph\0403044v1
L. Viola, H. Barnum, Entanglement and Subsystems, Entanglement beyond Subsystems, and All That; arxiv: quant-ph/070112v1
January 12, 2010: Discussion
Time and Location: Tuesday, Jan 12, 4pm, Hennings 311