Research lectures, seminars and events
The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but wish to enquire about attending one of the events please contact the organiser or host department.
|October 2018||December 2018|
Events for 20 November 2018
I will begin with an introduction about how to attach 2-dimensional representations of Galois groups to modular forms, both in positive and null characteristic, focusing on the important special case of elliptic curves. It turns out that the phenomenon of "complex multiplication", whose definition I will recall, can be read in the shape of the image of the representation. I will then discuss a recent result, obtained with N. Billerey (Clermont-Ferrand), ensuring that if a modular form behaves as having complex multiplication when reduced modulo a certain prime p, then it is congruent (mod p) to another form which truly has complex multiplication.
Software for quantum computation has a layered structure. Closest to the hardware, and strongly device-dependent, is the `quantum control’ of physical qubits. One layer up is the compilation of `native’ quantum gates into a universal gate library and quantum circuits of increasing complexity. The top layer is a quantum algorithm for a concrete computational task. Recent experimental progress has allowed the execution of all layers of this software stack, and the comparison of the performance of different qubit platforms.
In most cases, quantum control is played out through one and two-qubit operations. We present a framework for quantum control directly at the level of N qubits, relying on ideas from quantum many-body theory. An example is a protocol for a gate called iSWAPn, using a linear qubit array with so-called Krawtchouk couplings.