Search complexity and resource scaling for the quantum optimal control of unitary transformations

Journal Article · Sat Jan 15 04:00:00 EST 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.012326· OSTI ID:21529059

Moore, Katharine W; Riviello, Gregory; Rabitz, Herschel ^[1]; Chakrabarti, Raj ^[1]

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1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States)

The optimal control of unitary transformations is a fundamental problem in quantum control theory and quantum information processing. The feasibility of performing such optimizations is determined by the computational and control resources required, particularly for systems with large Hilbert spaces. Prior work on unitary transformation control indicates that (i) for controllable systems, local extrema in the search landscape for optimal control of quantum gates have null measure, facilitating the convergence of local search algorithms, but (ii) the required time for convergence to optimal controls can scale exponentially with the Hilbert space dimension. Depending on the control-system Hamiltonian, the landscape structure and scaling may vary. This work introduces methods for quantifying Hamiltonian-dependent and kinematic effects on control optimization dynamics in order to classify quantum systems according to the search effort and control resources required to implement arbitrary unitary transformations.

• OSTI ID: 21529059
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 83; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BANACH SPACE
CONTROL
CONTROL SYSTEMS
CONTROL THEORY
CONVERGENCE
DATA PROCESSING
HAMILTONIANS
HILBERT SPACE
INFORMATION
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
OPTIMAL CONTROL
OPTIMIZATION
PROCESSING
QUANTUM INFORMATION
QUANTUM OPERATORS
SCALING
SPACE
TRANSFORMATIONS