Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates

TL;DR

This paper demonstrates through analytical and numerical methods that the control landscape for ultrafast single-qubit phase shift gates is free of traps, enabling optimal quantum control in minimal time.

Contribution

It provides the first rigorous proof that the control landscape for ultrafast phase shift gates has no traps, extending previous results to this specific quantum gate.

Findings

Control landscape for ultrafast phase shift gates is trap-free.

Combination of analytical and numerical methods confirms trap absence.

Supports efficient optimal control of quantum gates in minimal time.

Abstract

In this work, we consider the problem of ultrafast controlled generation of single-qubit phase shift quantum gates. Globally optimal control is a control which realizes the gate with maximal possible fidelity. Trap is a control which is optimal only locally but not globally. It was shown before that traps do not exist for controlled generation of arbitrary single-qubit quantum gates for sufficiently long times, as well as for fast control of quantum gates other than phase shift gates. Ultrafast generation of phase-shift gates was missed in the previous analysis. In this work we show, combining analytical and numerical optimization methods such as Gradient Ascent Pulse Engineering (GRAPE), differential evolution, and dual annealing, that control landscape for ultrafast generation of phase shift gates is also free of traps. Mathematical analysis of quantum control landscapes, which aims to prove either absence or existence of traps for quantum control objective functionals, is an important topic in quantum control. In this work, we provide a rigorous analysis of quantum control landscapes for ultrafast generation of single-qubit quantum gates and show, combining analytical methods based on a sophisticated analysis of spectrum of the Hessian, and numerical optimization methods such as Gradient Ascent Pulse Engineering (GRAPE), differential evolution, and dual annealing, that control landscape for ultrafast generation of phase shift gates is free of traps.