Browsing Combinatorics and Optimization by Subject "quantum"
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Approximate Private Quantum Channels
(University of Waterloo, 2006)This thesis includes a survey of the results known for private and approximate private quantum channels. We develop the best known upper bound for ε-randomizing maps, <em>n</em> + 2log(1/ε) + <em>c</em> ... -
Characterization of non-universal two-qubit Hamiltonians
(University of Waterloo, 2009-12-16)It is known that almost all 2-qubit gates are universal for quantum computing (Lloyd 1995; Deutsch, Barenco, Eckert 1995). However, an explicit characterization of non-universal 2-qubit gates is not known. We consider a ... -
Continuous-time Quantum Algorithms: Searching and Adiabatic Computation
(University of Waterloo, 2002)One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum ... -
On the Power and Limitations of Shallow Quantum Circuits
(University of Waterloo, 2022-09-01)Constant-depth quantum circuits, or shallow quantum circuits, have been shown to exhibit behavior that is uniquely quantum. This thesis explores the power and limitations of constant-depth quantum circuits, in particular ...