Computational power of infinite quantum parallelism

Abstract

Recent works have independently suggested that quantum mechanics might permit procedures that fundamentally transcend the power of Turing Machines as well as of 'standard' Quantum Computers, These approaches rely on and indicate that quantum mechanics seems to support some infinite variant of classical parallel computing. We compare this new one with other attempts towards hypercomputation by separating (1) its computing capabilities from (2) realizability issues. The first are shown to coincide with recursive enumerability; the second are considered in analogy to 'existence' in mathematical logic. © 2005 Springer Science+Business Media, Inc.