**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

Monday, April 1, 2019 10:00 AM EDT

MC 5417

Jaron Huq | Applied Math, University of Waterloo

Three Results in Quantum Physics

This thesis is split into three disjoint sections. The ﬁrst deals with two practical issues regarding the use of unitary 2-designs. A simpliﬁed description of how to generate elements of the smallest known unitary 2-design on qubits is given which should be usable even for people who do not have much experience with the mathematics of ﬁnite ﬁelds. The section also gives a new way to decompose an arbitrary element of the Cliﬀord group into one and two qubit gates and is by far the simplest decomposition of its kind. The second section describes similarities and diﬀerences between a probabilistic formulation of classical mechanics and quantum mechanics, with the intention that it could become a resource for physics students to show that just because a physical phenomenon is strange it is not necessarily quantum. The third section is more speculative and delves into the relationship between a highly theoretical ﬁeld of quantum information science, Quantum Prover Interactive Proofs, and a highly practical area of quantum information science, error characterization. Previously unnoticed links are drawn between these ﬁelds with the intention that further research can provide fertile ground for both to ﬂourish.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

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