# Jon Yard

### Research Interests

My research focuses on mathematical aspects of quantum information and computation. I use information theory, number theory and geometry to study optimal and explicit codes and protocols for computing and for manipulating quantum information. Specific research interests include quantum Shannon theory, topological quantum computing, quantum field theory and the arithmetic of quantum circuits.

### Positions Held

- 2012 - 2016 Station Q / QuArC, Microsoft Research Postdoctoral Researcher
- 2007 - 2012 Los Alamos National Laboratory Postdoctoral Research Associate 3 years as Richard P. Feynman Postdoctoral Fellow
- 2005 - 2007 Institute for Quantum Information, Caltech Postdoctoral Scholar in Physics
- 2005 - 2005 Department of Computer Science, University of Montreal Academic Casual Researcher

### Recent Publications

- M. Appleby, G. McConnell, S. Flammia and J. Yard, Generating Ray Class Fields of Real Quadratic Fields via Complex Equiangular Lines, Acta Arithmetica 192, 2020, 211-233, arXiv: 1604.06098
- M. Appleby, S. Flammia, G. McConnell and J. Yard, SICs and algebraic number theory, Foundations of Physics. 47(8), 2017, pp 1042-1059, arXiv: 1701.05200

### Seminars

- Algebraic formulations of Zauner's conjecture. Combinatorics and Optimization Tutte Colloquium, University of Waterloo, ON
- Tight 2-designs in projective spaces. Open Problems in Algebraic Combinatorics (online), University of Waterloo, ON
- Fault-tolerant gates: Constructions, applications and challenges. IQC Faculty Seminar, University of Waterloo, ON.
- Quantum gates, class fields and SIC-POVMs. Workshop on Quantum Information and Holography. University of Windsor, ON
- "On the existence of SIC-POVMs", IAMCS Workshop on Quantum Computation and Information, College Station, TX
- The number theory of quantum information, RAC Seminar, Waterloo, ON
- On the existence of symmetric quantum measurements, AMS Spring Eastern Sectional Meeting, Boston MA.
- The number theory of equiangular lines, Combinatorics & Optimization Tutte Colloquium, Waterloo, ON
- On the exitence of symmetric quantum measurements, CMS Winter Meeting, Waterloo, ON.
- Quantum gates and arithmetic. Turing Inc Workshop on Near-term Quantum Computing, Calistoga, CA
- Topological phases and arithmetic. Special Session on Mathematics of Quantum Phases of Matter and Quantum Information, Mathematical Congress of the Americas, Montreal, QC
- Evidence for SIC-POVMs from class field theory. Probabilistic and Algebraic Methods in Quantum Information Theory, College Station, TX
- Lines, designs and quantum mechanics over class fields. International Workshop on Quantum Physics and Geometry, Levico Terme, Italy
- Equiangular complex projective 2-designs. University of Waterloo algebraic graph theory seminar, University of Waterloo, Waterloo, ON
- From classical to quantum Shannon theory. Combinatorics & Optimization Tutte Colloquium, University of Waterloo, Waterloo, ON
- Complex equiangular lines and class field theory. University of Waterloo geometry seminar, Waterloo ON
- SIC-POVMs and algebraic number theory. AMS Special Session on Topological Phases of Matter and Quantum Computation, Brunswick, ME
- Quadratic forms on Hermitian matrices. Workshop on Representation Theory in Quantum Information, Guelph, ON
- SICs, harmonic invariants and integer Liouville background charges, Quantum Information Group Meeting
- Can quantum field theory clarify the number theory of optimal quantum measurements?, PI Day
- PIRSA:17100080, Explicit class field theory from quantum measurements, 2017-10-16, Mathematical Physics
- PIRSA:16060049, Quantum gates, 2016-06-08, Colloquium
- PIRSA:12030092, Quantifying Entanglement with Quantum Entropy, 2012-03-07, Colloquium
- PIRSA:08120029, Surprises in the theory of quantum channel capacity, 2008-12-09, Young Researchers Conference 2008
- PIRSA:08090021, Quantum communication with zero-capacity channels, 2008-09-24, Perimeter Institute Quantum Discussions