On extrema of the objective functional for short-time generation of single qubit quantum gates

Abstract

In the present work the extrema of the objective functional for the problem of generation of quantum gates (logical elements for quantum computations) for two--level systems are investigated for short duration of the control. The problem of existence of local but not global extrema, the so called traps, is considered. In prior works the absence of traps was proved for a sufficiently long control duration. In this paper we prove that for almost all target unitary operators and system Hamiltonians traps are absent for an arbitrarily small control duration. For the remainder target unitary operators and Hamiltonians we obtain a new estimate for the lower boundary of the control duration which guarantees the absence of traps.

References in corpus (2)

• Control landscapes for two-level open quantum systems
• Trap-free manipulation in the Landau-Zener system

Cited by in corpus (4)

• Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search
• 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