Can Quantum Mechanics Be Reconciled with Cellular Automata?

Zohre Beiki, Ali Shahidinejad

An Introduction to Quantum Cellular Automata Technology and Its Defects

Peter J. Love

Jincheng Zhang

Quantum-enhanced simulation of cellular automata aims to surpass current limitations by leveraging quantum mechanics to model emergent behavior at a fundamental level within cellular automata. This paper introduces a novel algorithm for simulating long-term evolution of cellular automata patterns, incorporating quantum state evolution to enhance accuracy and potentially unlock novel emergent properties. The core mechanism involves implementing a quantum-enhanced 'quantum state evolution' process to simulate the long-term dynamics of cellular automata. Current cellular automata simulations often rely on approximations, while quantum enhancement offers a more accurate representation of complex system dynamics. This research explores the potential of quantum mechanics to fundamentally alter the simulation process, leading to more realistic and insightful models.

Hans-Thomas Elze

We consider discrete and integer-valued cellular automata (CA). A particular class of which comprises "Hamiltonian CA" with equations of motion that bear similarities to Hamilton's equations, while they present discrete updating rules. The dynamics is linear , quite similar to unitary evolution described by the Schrödinger equation. This has been essential in our construction of an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental discreteness scale. Based on Shannon's sampling theory, it leads, for example, to a one-to-one relation between quantum mechanical and CA conservation laws. The important issue of linearity of the theory is examined here by incorporating higher-order nonlinearities into the underlying action. These produce inconsistent nonlocal (in time) effects when trying to describe continuously such nonlinear CA. Therefore, in the present framework, only linear CA and local quantum mechanical dynamics are compatible.

Pablo J. Arrighi

Stefano Forti