Construction of Arbitrary Robust One-Qubit Operations Using Planar Geometry

TL;DR

This paper presents a planar geometry-based method for constructing arbitrary robust one-qubit operations using simple control Hamiltonians, achieving efficiency comparable to the shortest known composite pulses.

Contribution

It introduces a novel geometric approach for designing robust one-qubit gates with simple control Hamiltonians, improving interpretability and efficiency.

Findings

Constructs arbitrary robust one-qubit gates using planar geometry.

Achieves total execution time comparable to shortest known sequences.

Uses piecewise constant control Hamiltonians for simplicity.

Abstract

We show how to construct an arbitrary robust one-qubit unitary operation with a control Hamiltonian of $A_x(t) \sigma_x + A_y(t) \sigma_y$, where $\sigma_i$ is a Pauli matrix and $A_i(t)$ is piecewise constant. Our method, based on planar geometry, admits a simple and intuitive interpretation. Furthermore, the total execution time and the number of elementary gates of the obtained sequence are comparable to those of the shortest known concatenated composite pulses.