Quantum causal graph dynamics

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 18 Jul 2017Embargo end date: 01 Jan 2016 France English Publisher:American Physical Society (APS)Journal:Physical Review D, volume 96 (issn: 2470-0010, eissn: 2470-0029,

Copyright policy )Funded by:ANR | CausaQ

Authors: Arrighi, Pablo; Martiel, Simon;

doi: 10.1103/physrevd.96.024026 , 10.48550/arxiv.1607.06700

arXiv: 1607.06700

Quantum causal graph dynamics

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Abstract

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. Keywords: Quantum Lattice Gas Automata, Block-representation, Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum Graphity, Causal Dynamical Triangulations, Spin Networks, Dynamical networks, Graph Rewriting.

8 pages, 1 figure

Country

France

Related Organizations

French Institute for Research in Computer Science and Automation
France
French National Centre for Scientific Research
France
Centrale Marseille
France
Grenoble Alpes University
France
Inria Saclay - Île-de-France Research Centre
France

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Keywords

Quantum Gravity, FOS: Computer and information sciences, causality, Quantum Graphity, Discrete Mathematics (cs.DM), Block-representation, No-signalling, Curtis-Hedlund-Lyndon, FOS: Physical sciences, triangulation, General Relativity and Quantum Cosmology (gr-qc), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO] Computer Science [cs], spin, General Relativity and Quantum Cosmology, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Dynamical networks, Localizability, gas, gate, unitarity, Causal Dynamical Triangulations, time, [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Graph Rewriting, lattice, Quantum Physics, [PHYS.GRQC] Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], superposition, F.1.1; F.1.2, Quantum Lattice Gas Automata, 004, [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], quantum gravity, network, [PHYS.GRQC]Physics [physics]/General Relativity and Quantum Cosmology [gr-qc], discrete, time dependence, Spin Networks, F.1.2, Quantum Physics (quant-ph), F.1.1, Computer Science - Discrete Mathematics

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