This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts. The unique characteristics of quantum theory may also be used to create a quantum associative memory with a capacity exponential in the number of neurons. This paper combines two quantum computational algorithms to produce such a quantum associative memory. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. The paper covers necessary high-level quantum mechanical and quantum computational ideas and introduces a quantum associative memory. Theoretical analysis proves the utility of the memory, and it is noted that a small version should be physically realizable in the near future.

Liquid chromatography-mass spectrometry is widely used for comparative replicate sample analysis in proteomics, lipidomics and metabolomics. Before statistical comparison, registration must be established to match corresponding analytes from run to run. Alignment, the most popular correspondence approach, consists of constructing a function that warps the content of runs to most closely match a given reference sample. To date, dozens of correspondence algorithms have been proposed, creating a daunting challenge for practitioners in algorithm selection. Yet, existing reviews have highlighted only a few approaches. In this review, we describe 50 correspondence algorithms to facilitate practical algorithm selection. We elucidate the motivation for correspondence and analyze the limitations of current approaches, which include prohibitive runtimes, numerous user parameters, model limitations and the need for reference samples. We suggest and describe a paradigm shift for overcoming current correspondence limitations by building on known liquid chromatography-mass spectrometry behavior.

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BRIGHAM YOUNG UNIVERSITY As chair of the candidate's graduate committee, I have read the thesis of R. David Norton in its final form and have found that (1) its format, citations, and bibliographical style are consistent and acceptable and fulfill university and department style requirements; (2) its illustrative materials including figures, tables, and charts are in place; and (3) the final manuscript is satisfactory to the graduate committee and is ready for submission to the university library.