Purifying Quantum States: Quantum and Classical Algorithms

I give analytical estimates and numerical simulation results for the performance of Kitaev's 2d topological error-correcting codes. By providing methods for the execution of an encoded three-qubit Toffoli gate, I complete a universal gate set for these codes. I also examine the utility of Bohm's and Bohm-inspired interpretations of quantum mechanics for numerical solution of many-body dynamics and ``mechanism identification'' heuristics in discrete systems. Further, I show an unexpected quantitative correspondence between the previously known continuum of stochastic-Bohm trajectory theories on the one hand and extant path integral Monte Carlo methods on the other hand.