If we look at Frobenius’s theorem, this suggests that we should focus on the subgroups of a fixed Sylow p-subgroup P , and all of the conjugation maps cg for the various g ∈ G between the subgroups of P . Often, if g ∈ G and Q 6 P , Q · cg = Q does not lie inside P , and so we simply ignore those maps, and only keep the ones where both the domain and the image are inside P . This leads us to de...

We introduce a generalized method of holonomic quantum computation (HQC) based on encoding in subsystems. As an application, we propose a scheme for applying holonomic gates to unencoded qubits by the use of a noisy ancillary qubit. This scheme does not require initialization in a subspace since all dynamical effects factor out as a transformation on the ancilla. We use this approach to show ho...

With the unprecedented proliferation of high-speed communication services many people will have high-speed access to virtually unlimited amounts of information in many forms of media. A tremendous amount of research effort is being applied to the problems of how to provide these multi-media services to tens and hundreds of thousands of concurrent users. The I/O problems alone are significant an...

Abstract We bound the number of distinct minimal subsystems a given transitive subshift linear complexity, continuing work Ormes and Pavlov [On complexity function for sequences which are not uniformly recurrent. Dynamical Systems Random Processes (Contemporary Mathematics, 736) . American Mathematical Society, Providence, RI, 2019, pp. 125--137]. also generic measures such can support based on...