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- Jon Yard

My research is in quantum information science, an interdisciplinary subject using ideas and methods from physics, mathematics and computer science to study information and computation in light of quantum mechanics. A central goal of my research is to determine the ultimate capabilities and limitations of computers, networks and other physical systems for computing and for processing information. Through my research, I want to gain a better understanding of the true physical nature of information and to make significant theoretical advances toward realizing a fault-tolerant quantum computer. My approach is two-fold: On one hand, I use mathematical tools, such as algebraic number theory, to study explicit constructions and algorithms for fault-tolerant quantum gates in finite dimensions. On the other hand, I use traditional information-theoretic methods, like random coding, to answer fundamental questions about entanglement, correlations and error correction in the asymptotic limit of arbitrarily many quantum systems. I also work at the interface between these complementary yet interrelated approaches, such as on arithmetical aspects of the quantum Hall effect and other topological phases in 2+1 dimensions. Besides helping to classify such theories, this may lead to new ways of thinking about the complexity of physical systems, to new quantum algorithms, or to new perspectives on quantum field theory.

- 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

- M. Appleby, S. Flammia, G. McConnell and J. Yard, SICs and algebraic number theory, Foundations of Physics. 47(8), April 24, 2017, pp 1042-1059, arXiv: 1701.05200
- Generating Ray Class Fields of Real Quadratic Fields via Complex Equiangular Lines, M. Appleby, G. McConnell, S. Flammia and J. Yard, arXiv: 1604.06098v2 (submitted to Mathematical Proceedings of the Cambridge Philosophical Society)

- 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

©2012 Perimeter Institute for Theoretical Physics