Coherent control of a qubit is trap-free

Abstract

There is a strong interest in optimal manipulating of quantum systems by external controls. Traps are controls which are optimal only locally but not globally. If they exist, they can be serious obstacles to the search of globally optimal controls in numerical and laboratory experiments, and for this reason the analysis of traps attracts considerable attention. In this paper we prove that for a wide range of control problems for two-level quantum systems all locally optimal controls are also globally optimal. Hence we conclude that two-level systems in general are trap-free. In particular, manipulating qubits---two-level quantum systems forming a basic building block for quantum computation---is free of traps for fundamental problems such as the state preparation and gate generation.

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Cited by in corpus (9)

• Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates
• Control landscape for ultrafast manipulation by a qubit
• Control of quantum transmission is trap free
• On extrema of the objective functional for short-time generation of single qubit quantum gates
• Constraint optimization and $\mathcal{S}\mathcal{U}(N)$ quantum control landscapes
• On critical points of the objective functional for maximization of qubit observables
• On optimization of coherent and incoherent controls for two-level quantum systems
• On the detailed structure of quantum control landscape for fast single qubit phase-shift gate generation
• Quantum Control Landscapes Beyond the Dipole Approximation