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Friday, July 3, 2020 — 3:30 PM EDT
Title: Number-theoretic methods in quantum computing
| Speaker: | Peter Selinger |
| Affiliation: | Dalhousie University |
| Zoom: | Please email Emma Watson |
Abstract:
An important problem in quantum computing is the so-called \emph{approximate synthesis problem}: to find a quantum circuit, preferably as short as possible, that approximates a given target operation up to given $\epsilon$. For nearly two decades, from 1995 to 2012, the standard solution to this problem was the Solovay-Kitaev algorithm, which is based on geometric ideas. This algorithm produces circuits of size $O(\log^c(1/\epsilon))$, where $c$ is a constant approximately equal to $3.97$. It was a long-standing open problem whether the exponent $c$ could be reduced to $1$.
Monday, July 6, 2020 — 11:30 AM EDT
Title: A covering graph perspective on Huang’s theorem
| Speaker: | Maxwell Levit |
| Affiliation: | University of Waterloo |
| Zoom: | Contact Soffia Arnadottir |
Abstract:
Just about a year ago, Hao Huang resolved the sensitivity conjecture by proving that any induced subgraph on more than half the vertices of the hypercube $Q_n$ has maximum degree at least $\sqrt(n)$. The key ingredient in his proof is a special $\pm 1$ signing of the adjacency matrix of $Q_n$.
Thursday, July 9, 2020 — 2:30 PM EDT
Title: Formulas for Macdonald polynomials arising from the ASEP
| Speaker: | Olya Mandelshtam |
| Affiliation: | Brown University |
| Zoom: | Contact Karen Yeats |
Abstract:
The asymmetric simple exclusion process (ASEP) is a one-dimensional model of hopping particles that has been extensively studied in statistical mechanics, probability, and combinatorics. It also has remarkable connections with orthogonal symmetric polynomials in many variables such as Macdonald and Koornwinder polynomials.
Friday, July 10, 2020 — 3:30 PM EDT
Title: Number-theoretic methods in quantum computing
| Speaker: | Felix Leditzky |
| Affiliation: | University of Waterloo |
| Zoom: | Please email Emma Watson |
Abstract:
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. The original teleportation protocol is an exact protocol and amazingly simple, but it requires a non-trivial correction operation to make it work. Port-based teleportation (PBT) is an approximate variant of teleportation with a simple correction operation that renders the protocol unitarily covariant.