A geometric view of quantum cellular automata

Jonathan R. McDonald, Paul M. Alsing, Howard A. Blair

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Nielsen, et al. 1, 2 proposed a view of quantum computation where determining optimal algorithms is equivalent to extremizing a geodesic length or cost functional. This view of optimization is highly suggestive of an action principle of the space of N-qubits interacting via local operations. The cost or action functional is given by the cost of evolution operators on local qubit operations leading to causal dynamics, as in Blute et. al. 3 Here we propose a view of information geometry for quantum algorithms where the inherent causal structure determines topology and information distances 4, 5 set the local geometry. This naturally leads to geometric characterization of hypersurfaces in a quantum cellular automaton. While in standard quantum circuit representations the connections between individual qubits, i.e. the topology, for hypersurfaces will be dynamic, quantum cellular automata have readily identifiable static hypersurface topologies determined via the quantum update rules. We demonstrate construction of quantum cellular automata geometry and discuss the utility of this approach for tracking entanglement and algorithm optimization.

Original languageEnglish (US)
Title of host publicationQuantum Information and Computation X
DOIs
StatePublished - Jul 23 2012
EventQuantum Information and Computation X - Baltimore, MD, United States
Duration: Apr 26 2012Apr 27 2012

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume8400
ISSN (Print)0277-786X

Other

OtherQuantum Information and Computation X
CountryUnited States
CityBaltimore, MD
Period4/26/124/27/12

Keywords

  • Information geometry
  • Quantum cellular automata
  • Quantum computation
  • Quantum information

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    McDonald, J. R., Alsing, P. M., & Blair, H. A. (2012). A geometric view of quantum cellular automata. In Quantum Information and Computation X [84000S] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 8400). https://doi.org/10.1117/12.921329