New Models of Computation

Richard Charles Murphy

Goos, Gerhard, Jan Van Leeuwen, Hartmanis, Juris

Andris Ambainis, Abuzer Yakaryılmaz

Quantum computing is a new model of computation, based on quantum physics.Quantum computers can be exponentially faster than conventional computers for problems such as factoring.Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied.In this paper, we survey various models of quantum finite automata and their properties.We also provide some open questions and new directions for researchers.

Cristian S. Calude, John L. Casti, MJ Dinneen

Masanori Ohya, Igor Vasil'evich Volovich

A new model for computations is considered which combines the quantum computer with the chaotic dynamics amplifier, based on the logistic map. We discuss the satisfiability problem and argue that the problem can, in principle, be solved in polynomial time if one uses the new model for computations.

William J. Zeng

We construct abstract models of blackbox quantum algorithms using a model of quantum computation in sets and relations, a setting that is usually considered for nondeterministic classical computation. This alternative model of quantum computation (QCRel), though unphysical, nevertheless faithfully models its computational structure. Our main results are models of the Deutsch-Jozsa, single-shot Grovers, and GroupHomID algorithms in QCRel. These results provide new tools to analyze the semantics of quantum computation and improve our understanding of the relationship between computational speedups and the structure of physical theories. They also exemplify a method of extending physical/computational intuition into new mathematical settings.