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

UR - http://www.scopus.com/inward/record.url?scp=84863933245&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863933245&partnerID=8YFLogxK

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 -