Algorithmic Cooling and Scalable NMR Quantum Computers

We present here algorithmic cooling (via polarization-heat-bath)- a powerful method for obtaining a large number of highly polarized spins in liquid nuclear-spin systems at finite temperature. Given that spin-half states represent (quantum) bits, algorithmic cooling cleans dirty bits beyond the Shannon's bound on data compression, by employing a set of rapidly thermal-relaxing bits. Such auxiliary bits could be implemented using spins that rapidly get into thermal equilibrium with the environment, e.g., electron spins. Cooling spins to a very low temperature without cooling the environment could lead to a breakthrough in nuclear magnetic resonance experiments, and our ``spin-refrigerating'' method suggests that this is possible. The scaling of NMR ensemble computers is probably the main obstacle to building useful quantum computing devices, and our spin-refrigerating method suggests that this problem can be resolved.Comment: 21 pages, 3 figure

MODES OF ENGAGEMENT: MULTI-MODAL CURRICULUM AND INSTRUCTION; A SCHOOL-WIDE CURRICULAR DESIGN WITHOUT TEXTBOOKS

One of the most challenging aspects of teaching and studying teaching is that the domain of teaching is so complex. This complexity has made it difficult for teachers to design curriculum and critique that evolving curriculum through ongoing reconsideration and revision in order to improve the effectiveness of instruction. An alternative curricular/instructional construct, called Modes of Engagement, was created and has been sustained for 24 years, by the principal and faculty at Desert Willow Family School, a K-8 Albuquerque Public Schools\u27 alternative school. The Modes of Engagement, as they are employed in the teaching of mathematics at Family School, are explored in this study, from their origins to their current iterations. By designing the mathematics curriculum in segments that reflect varying purposes, and simultaneously matching the modes\u27 instructional practices to these purposes, students at the school have flourished in mathematics while experiencing themselves as mathematicians. This self-study\u27s autobiography and document analysis will reveal how these modes have stood up to the testing pressures and restrictive views of content driven by accountability based on the mandated testing under No Child Left Behind (NCLB). There were consequences for our students under this testing pressure. Within the two to three-year gap of having discontinued two of the school\u27s math modes, students lost the ability to deal with ambiguity, challenges, tolerance for multiple methods, and enthusiasm for learning. This study reveals the evolution of the Modes of Engagement, including the ways in which their development and implementation has been influenced by both internal and external forces of the school. The Modes of Engagement offer a unique framework for considering school-based curriculum design; the history of the evolution of the Modes offers insight into the forces that foster or impede teacher initiative in curriculum design

Glosarium Matematika

273 p.; 24 cm