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Abstract:

Since 2005, there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as nuclear magnetic resonance quantum information processors. These approaches, which build on the original gradient ascent pulse engineering algorithm, remain computationally intensive because of the need to calculate matrix exponentials for each time step in the control pulse. In this study, we discuss how the propagators for each time step can be approximated using the Trotter–Suzuki formula, and a further speedup achieved by avoiding unnecessary operations. The resulting procedure can provide substantial speed gain with negligible costs in the propagator error, providing a more practical approach to pulse engineering.

Abstract:

Legislative amendment poses a conundrum: why do governments amend legislation that they only recently drafted? An effective method for quantifying amendments across a wide range of policy areas and legislatures would be valuable for answering such questions. Existing studies almost all rely on hand-counting and coding of amendments, methods which are laborious, necessarily subjective, and difficult to replicate. Using insights from bioinformatics (the study of genetic codes), we developed a streamlined method to quantify and visualise the amount of amendment. In an exploratory study of three parliamentary sessions since 2008, we found that UK legislation was considerably amended and lengthened during the parliamentary process. We discuss our results in the light of theories of information asymmetries between the government and the legislature.