Quantum Causal Graph Dynamics

Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose,...

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Bibliographic Details
Published in:Physical review. D 2017, Vol.96 (2)
Main Authors: Arrighi, Pablo, Martiel, Simon
Format: Article
Language:English
Subjects:
Computer Science
Discrete Mathematics
General Relativity and Quantum Cosmology
Physics
Quantum Physics
Online Access:Get full text
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Summary:Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs—in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on quantum cellular automata with another on reversible causal graph dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. We discuss some of the implications for quantum gravity.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.96.024026