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Full-Text Articles in Physics
Combinatorial Algorithms For Perturbation Theory And Application On Quantum Computing, Yudong Cao
Combinatorial Algorithms For Perturbation Theory And Application On Quantum Computing, Yudong Cao
Open Access Dissertations
Quantum computing is an emerging area between computer science and physics. Numerous problems in quantum computing involve quantum many-body interactions. This dissertation concerns the problem of simulating arbitrary quantum many-body interactions using realistic two-body interactions. To address this issue, a general class of techniques called perturbative reductions (or perturbative gadgets) is adopted from quantum complexity theory and in this dissertation these techniques are improved for experimental considerations. The idea of perturbative reduction is based on the mathematical machinery of perturbation theory in quantum physics. A central theme of this dissertation is then to analyze the combinatorial structure of the perturbation …
Directed Percolation And The Abstract Tile Assembly Model, Tyler Garrett Moore
Directed Percolation And The Abstract Tile Assembly Model, Tyler Garrett Moore
Graduate Theses and Dissertations
Self-assembly is a process by which simple components build complex structures through local interactions. Directed percolation is a statistical physical model for describing competitive spreading processes on lattices. The author describes an algorithm which can transform a tile assembly system in the abstract Tile Assembly Model into a directed percolation problem, and then shows simulations of the aTAM which support this algorithm. The author also investigates two new constructs designed for Erik Winfree's abstract Tile Assembly Model called the NULL tile and temperature 1.5. These constructs aid the translation between self-assembly and directed percolation and may assist self-assembly researchers in …