Generalized Partitioned Quantum Cellular Automata and Quantization of Classical CA

TL;DR

This paper introduces a new framework for partitioned quantum cellular automata (QCA), establishing conditions for their formation from classical cellular automata (CA) and presenting simulation results of quantumization.

Contribution

It proposes a generalized formulation of partitioned QCA and conditions for their well-formedness derived from classical CA, advancing the understanding of quantum-classical CA relationships.

Findings

Established conditions for local transition functions in QCA

Extended classical CA to quantumized versions under specific conditions

Presented simulation results demonstrating quantumization of classical CA

Abstract

In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstrate the condition of local transition functions, which induce a global transition of well-formed QCA. Following the results, extending a natural correspondence of classical cells and quantum cells to the correspondence of classical CA and QCA, we have the condition of classical CA such that CA generated by quantumization of its cells is well-formed QCA. Finally we report some results of computer simulations of quantumization of classical CA.