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IEEE Transactions on Control Systems Technology

Lyapunov Control of Quantum Systems Based on Energy-Level Connectivity Graphs

Sen Kuang, Daoyi Dong, Ian R. Petersen

Published Oct 4, 2018• 29 citations
Publisher

Abstract

This paper proposes a new multilayer Lyapunov control scheme based on energy-level connectivity graphs of quantum systems, which enables a high-probability population transfer to any eigenstate in high-dimensional quantum systems. We provide a graph connectivity result for stability analysis and explore the selectivity characteristic of the Lyapunov control fields. A systematic layering method for the energy-level connectivity graph is presented to achieve a layer-by-layer population transfer to the target state. Several applications including a five-level quantum system, a three-qubit superconducting system, and a spin chain of five qubits are presented to demonstrate the effectiveness of the multilayer Lyapunov control method.

DOI
10.1109/tcst.2018.2871186

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Based on the analysis of the invariant set in quantum Lyapunov control under a performance index with degrees of freedom, the population control of eigenstates is studied. For isolated target eigenstates, this paper shows the existence of the degrees of freedom that guarantee exact convergence and obtains rigorous construction relation of those degrees of freedom. For non-isolated target eigenstates, we propose a path-planning-based method. The method considers transition paths of controlled systems, so can achieve intuitive and high-probability transition to desired target eigenstate accompanied with appropriate design of those degrees of freedom.
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