TY - GEN
T1 - A geometric view of quantum cellular automata
AU - McDonald, Jonathan R.
AU - Alsing, Paul M.
AU - Blair, Howard A.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - Information geometry
KW - Quantum cellular automata
KW - Quantum computation
KW - Quantum information
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U2 - 10.1117/12.921329
DO - 10.1117/12.921329
M3 - Conference contribution
AN - SCOPUS:84863933245
SN - 9780819490780
T3 - Proceedings of SPIE - The International Society for Optical Engineering
BT - Quantum Information and Computation X
T2 - Quantum Information and Computation X
Y2 - 26 April 2012 through 27 April 2012
ER -