Role of controllability in optimizing quantum dynamics

Journal Article · Wed Jun 15 04:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.062306· OSTI ID:21550056

Rebing, Wu; Hsieh, Michael A; Rabitz, Herschel ^[1]

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1. Department of Automation, Tsinghua University, Beijing, 100084, China and Center for Quantum Information Science and Technology, TNList, Beijing, 100084 (China)

This paper reveals an important role that controllability plays in the complexity of optimizing quantum control dynamics. We show that the loss of controllability generally leads to multiple locally suboptimal controls when gate fidelity in a quantum control system is maximized, which does not happen if the system is controllable. Such local suboptimal controls may attract an optimization algorithm into a local trap when a global optimal solution is sought, even if the target gate can be perfectly realized. This conclusion results from an analysis of the critical topology of the corresponding quantum control landscape, which refers to the gate fidelity objective as a functional of the control fields. For uncontrollable systems, due to SU(2) and SU(3) dynamical symmetries, the control landscape corresponding to an implementable target gate is proven to possess multiple locally optimal critical points, and its ruggedness can be further increased if the target gate is not realizable. These results imply that the optimization of quantum dynamics can be seriously impeded when operating with local search algorithms under these conditions, and thus full controllability is demanded.

• OSTI ID: 21550056
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 6 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
ALGORITHMS
CONTROL
CONTROL SYSTEMS
LIE GROUPS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
OPTIMIZATION
QUANTUM MECHANICS
SU GROUPS
SU-2 GROUPS
SU-3 GROUPS
SYMMETRY GROUPS
TOPOLOGY