Finite Sample Analysis In Quantum Estimation PDF Download

Quantum computation is of great current interest in computer science, mathematics, physical sciences and engineering. The thesis is devoted to the statistical analysis of the model of quantum annealing, and statistical methodologies to construct density matrix estimators. The D-Wave One machine was announced in 2011 as "the world's first commercially available quantum computer" and claimed to run quantum annealing to solve optimization problem. Since the announcement, the model of the D-Wave One machine has been heavily debated. We conduct statistical analysis to compare the result of D-Wave One with the result of the simulated annealing, the simulated quantum annealing and a mean field approximation to quantum annealing. Our statistical analysis shows none of the simulated models fit the D-Wave model well. Meanwhile, comparison of plots and test statistics suggests the model of the D-Wave one is more or less similar to the simulated quantum annealing and the mean field approximation, while different from the simulated annealing. Density matrices describe the quantum states of quantum systems. It is important while difficult to estimate the density matrices, for the elements of density matrices cannot be measured directly. We propose statistical methodologies to construct density matrix estimators from quantum homodyne tomography measurements. We establish an asymptotic theory showing that the proposed density matrix estimators are consistent and have good convergence rates. A numerical study is conducted to demonstrate the finite sample performances of the proposed estimators.