Cellular automata machines: a new environment for modeling
Cellular automata machines: a new environment for modeling
A six-state minimal time solution to the firing squad synchronization problem
Theoretical Computer Science
Reversible simulation of one-dimensional irreversible cellular automata
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Reversible Cellular Automaton Able to Simulate Any Other Reversible One Using Partitioning Automata
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
Intrinsic Universality of a 1-Dimensional Reversible Cellular Automaton
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Inducing an Order on Cellular Automata by a Grouping Operation
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
On one-dimensional quantum cellular automata
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
From Dirac to Diffusion: Decoherence in Quantum Lattice Gases
Quantum Information Processing
Cellular Automata
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
One-Dimensional Quantum Cellular Automata over Finite, Unbounded Configurations
Language and Automata Theory and Applications
Universality in cellular automata
SWAT '70 Proceedings of the 11th Annual Symposium on Switching and Automata Theory (swat 1970)
Intrinsically Universal One-dimensional Quantum Cellular Automata in Two Flavours
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Partitioned quantum cellular automata are intrinsically universal
Natural Computing: an international journal
A simple n-dimensional intrinsically universal quantum cellular automaton
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
On the Circuit Depth of Structurally Reversible Cellular Automata
Fundamenta Informaticae
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Several non-axiomatic approaches have been taken to define Quantum Cellular Automata (QCA); Partitioned QCA (PQCA) are the most canonical. Here we show any QCA can be put into PQCA form. Our construction reconciles the non-axiomatic definitions of QCA, showing that they can all simulate one another, thus they are all equivalent to the axiomatic definition. A simple n-dimensional QCA capable of simulating all others to arbitrary precision is described, where the initial configuration and the evolution of any QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps then correspond to one step of the simulated QCA, achieved via a non-trivial reduction of the problem to universality in quantum circuits. Results are formalised by defining generalised n-dimensional intrinsic simulation, preserving topology in that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. Implications are discussed.