Other

Fault-tolerant quantum computers will compute by applying
a sequence of elementary unitary operations, or gates, to an
error-protected subspace.   While algorithms are typically expressed
over arbitrary local gates, there is unfortunately no known theory
that can correct errors for a continuous set of quantum gates.
However, theory does support the fault-tolerant construction of
various finite gate sets, which in some cases generate circuits that
can approximate arbitrary gates to any desired precision.   In this
talk, I will present a framework for approximating arbitrary qubit
unitaries over a very general but natural class of gate sets derived
from the theory of integral quaternions over number fields, where the
complexity of a unitary is algebraically encoded in the length of a
corresponding quaternion.  Then I will explore the role played by
higher-dimensional generalizations of the Pauli gates in various
physical and mathematical settings, from classifying bulk-boundary
correspondences of abelian fractional quantum Hall states to
generating optimal symmetric quantum measurements with surprising
connections to Hilbert's 12th problem on explicit class field theory
for real quadratic number fields.

Even the greatest scientists have made some serious blunders. "Brilliant Blunders" concerns the evolution of life on Earth, of the Earth itself, of stars, and of the universe as a whole.

In this talk, astrophysicist Dr. Mario Livio will explore and analyze major errors committed by such luminaries as Charles Darwin, Linus Pauling, and Albert Einstein. Dr. Livio will scrutinize the various types of blunders and attempt to explain how they happen. Blunders are not only inevitable, argues Dr. Livio, but also an integral component of the process of science.

100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago.  The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day. Although this event was but a blip in a sea of data taken by various experiments over the last several decades, it represents a paradigm shift in how we study our Universe.

In this colloquium, I will present some of the history of this great discovery and what it means for our future at the dawn of gravitational wave astronomy.