Since they were first envisioned, quantum computers have oft been portrayed as devices of limitless power, able to perform calculations in a mere instant that would take current computers years to determine. This is, of course, not the case. A huge amount of effort has been invested in trying to understand the limits of quantum computers---under which circumstances they outperform classical computers, how large a speed-up can be gained, and what draws the distinction between quantum and classical computing. In this Ph.D. thesis, I investigate a few intriguing properties of quantum computers involving quantum oracles and classically-simulatable quantum circuits. In Part I I study the notion of black-box unitary operations, and procedures for effecting the inverse operation. Part II looks at how quantum oracles can be used to test properties of probability distributions, and Part III considers classes of quantum circuits that can be simulated efficiently on a classical computer. In more detail, Part I studies procedures for inverting black-box unitary operations. Known techniques are generally limited in some way, often requiring ancilla systems, working only for restricted sets of operators, or simply being too inefficient. We develop a novel procedure without these limitations, and show how it can be applied to lift a requirement of the Solovay-Kitaev theorem, a landmark theorem of quantum compiling. Part II looks at property testing for probability distributions, and in particular considers a special type of access known as the \textit{conditional oracle}. The classical conditional oracle was developed by Canonne et al. in 2015 and subsequently greatly explored. We develop a quantum version of this oracle, and show that it has advantages over the classical process. We use this oracle to develop an algorithm that decides whether or not a mixed state is fully mixed. In Part III we study classically-simulatable quantum circuits in more depth. Two well-known classes are Clifford circuits and matchgate circuits, which we briefly review. Using these as inspiration, we use the Jordan-Wigner transform to develop new classes of non-trivial quantum circuits that are also classically simulatable.

There are three main factors affecting the stability of a palletized load that is unitized by a stretch wrapping mechanism. These factors include the type of unitized load, wrapping configuration and shipping method. The wrapping configuration is determined on the basis of the type of unitized load and shipping method. For this study, the aforementioned components were referred to as the package, the product, and the distribution environment. These components come together to make up a stretch wrapping system. The package corresponds to the stretch wrap film that is packaging the unitized load and pallet. The product corresponds to the goods placed on the pallet to be packaged by the stretch wrapper. The distribution environment corresponds to the hazards that the packaged product will encounter in transit. This study was designed to observe and understand the interactions between each of the components of the stretch wrap system. Prior to stretch wrapping a pallet of product, the film is elongated or pre-stretched. The elastic nature of the stretch wrap forces the film to conform around the palletized load. It is hypothesized that the film force that the stretch wrap applies to the palletized load contributes to improved load containment. Hence, the objective of this study was to determine the existence of a correlation between percentage pre-stretch to change in film force and load containment. For the study, a range of pre-stretched unitized loads were subjected to ISTA 3E distribution testing. Simultaneously the film force was monitored during the period of distribution testing. Subsequent to distribution testing, the load dispersion was quantified. The data obtained from this test suggested that there is no correlation between percentage pre-stretch and change in film force or load containment. The study also compared three methods of calculating pre-stretch: the marking wheel procedure, tapeless measure, and film cut and weigh. It was found that the most consistent method was the marking wheel procedure, followed by the cut and weigh procedure, and the tapeless measure procedure.

Quality, as well as stability of processes check is nowadays gaining on its significance. The main driving force of its increasing importance is the rapid expansion of series production. Large-scale manufacturing processes are concerned, in terms of the number of operators, direct and indirect influence on rejects, but also on process stability. There are several quality characteristics, defined by utility properties, that can be easily measurable (linear dimensions, solidity, elongation, humidity, concentration) or directly immeasurable, mostly subjective (fragrance, taste, color, comfort while using, appearance). Statistical Process Control-SPC features the preventive tool of quality control, because based on the early detection of significant divergences of the process from the predetermined level, it is possible to execute interventions in the process with the aim of maintaining the acceptable and stable level and improving the process. This manufacturing process check will be the topic of my thesis. At first, Shewhart's control charts analysis will be done to determine strong process instability. Consequently, analysis will be carried out in test chi-square, used to determine the influence of each factor on the process of stability (operators, type of shift, type of product, type of defect on the product). All the practical part will be processed in statistical software MINITAB15. The thesis will be complemented by the findings from the examination of the features of interval estimates of parameter p for binomial distribution - numeric stability in the various statistical software (specifically Minitab 15, Statistica, Matlab 7.8.0). Master's thesis was supported by project from MSMT of the Czech Republic no. 1M06047 Center for Quality and Reliability of Production.