# Jon Yard

### Research Interests

My research focuses on mathematical aspects of quantum information and computation. One goal is to make theoretical advances towards the realization of a fault-tolerant quantum computer. Another is to gain a better understanding of the physical nature of information, computation and complexity.
One direction of my research aims to characterize the optimal asymptotic rates for performing tasks like error correction, communication and entanglement manipulation in quantum systems. Another direction uses number theory and geometry to explore arithmetic aspects of gates, codes, algorithms and measurements for quantum systems. I am particularly interested in algebraic measures of complexity that exist in this setting, especially in ways they may relate to notions of complexity considered in high energy physics. I am also interested in various aspects of topological phases in 2+1D, from explicit realization in physical systems to the arithmetic of modular categories.

### 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

- 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
- 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