Complex Systems
Simulating quantum mechanics on a quantum computer
PhysComp96 Proceedings of the fourth workshop on Physics and computation
On L(d, 1)-labelings of graphs
Discrete Mathematics
A Decision Procedure for Well-Formed Linear Quantum Cellular Automata
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
Quantum Search of Spatial Regions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Locality and Information Transfer in Quantum Operations
Quantum Information Processing
From Dirac to Diffusion: Decoherence in Quantum Lattice Gases
Quantum Information Processing
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
Algebraic characterizations of unitary linear quantum cellular automata
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Partitioned quantum cellular automata are intrinsically universal
Natural Computing: an international journal
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Information and Computation
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We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution U. We require that this global evolution U be unitary, in accordance with quantum theory, and that this global evolution U be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of U. We show that under these conditions the operator U can be implemented locally; i.e. it can be put into the form of a quantum circuit made up with more elementary operators - each acting solely upon neighboring nodes. We take quantum cellular automata as an example application of this representation theorem: this analysis bridges the gap between the axiomatic and the constructive approaches to defining QCA.