Time-optimal Control of Independent Spin-1/2 Systems under Simultaneous Control

Abstract

We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction technique. We experimentally implement the optimal control using zero-field nuclear magnetic resonance. This reveals an average gate error of $1\%$ and a $70\%$ to $80$ $\%$ decrease in the experiment duration as compared to existing methods. This is the first analytical solution and experimental demonstration of time-optimal control in such a system and it provides a route to achieve time optimal control in more general quantum systems.

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Cited by in corpus (6)

• Interference in Atomic Magnetometry
• Minimum time generation of a uniform superposition in a qubit with only transverse field control
• Time optimal control based on classification of quantum gates
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Algorithms for Quantum Control without Discontinuities; Application to the Simultaneous Control of two Qubits
• Zero- to ultralow-field nuclear magnetic resonance and its applications