Three Results in Quantum Physics
Master's Candidate: Jaron Huq
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.
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