Orthologic and quantum logic: Models and computational elements

Abstract

Motivated by a growing need to understand the computational potential of quantum devices we suggest an approach to the relevant issues via quantum logic and its model theory. By isolating such notions as quantum parallelism and interference within a model-theoretic setting, quite divorced from their customary physical trappings, we seek to lay bare their logical underpinnings and possible computational ramifications. In the first part of the paper, a brief account of the relevant model theory is given, and some new results are derived. In the second part, we model the simplest classical gate, namely the N-gate, propose a quantization scheme (which translates between classical and quantum models, and from which emerges a logical interpretation of the notion of quantum parallelism), and apply it to the classical N-gate model. A class of physical instantiations of the resulting quantum N-gate model is also briefly discussed.