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Proceedings Paper

A geometric view of quantum cellular automata
Author(s): Jonathan R. McDonald; Paul M. Alsing; Howard A. Blair
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Paper 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 distances4, 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.

Paper Details

Date Published: 8 May 2012
PDF: 13 pages
Proc. SPIE 8400, Quantum Information and Computation X, 84000S (8 May 2012); doi: 10.1117/12.921329
Show Author Affiliations
Jonathan R. McDonald, Air Force Research Lab. (United States)
Paul M. Alsing, Air Force Research Lab. (United States)
Howard A. Blair, Syracuse Univ. (United States)

Published in SPIE Proceedings Vol. 8400:
Quantum Information and Computation X
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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