Noise-resistant Landau-Zener sweeps from geometrical curves

TL;DR

This paper introduces a geometrical approach to designing noise-robust Landau-Zener quantum control protocols, leveraging space curves to improve operation fidelity under noise conditions.

Contribution

It develops a novel method using space curves with constant torsion to create error-robust Landau-Zener sweeps, including non-monotonic drives for noise resilience.

Findings

Monotonic sweeps are not robust to noise in purely noise-induced avoided crossings.

Non-monotonic phase gates can be error-robust up to second order.

A general technique for designing robust protocols using space curves with constant torsion.

Abstract

Landau-Zener physics is often exploited to generate quantum logic gates and to perform state initialization and readout. The quality of these operations can be degraded by noise fluctuations in the energy gap at the avoided crossing. We leverage a recently discovered correspondence between qubit evolution and space curves in three dimensions to design noise-robust Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is purely noise-induced, we prove that operations based on monotonic sweeps cannot be robust to noise. Hence, we design families of phase gates based on non-monotonic drives that are error-robust up to second order. In the general case where there is an avoided crossing even in the absence of noise, we present a general technique for designing robust driving protocols that takes advantage of a relationship between the Landau-Zener problem and space curves of constant torsion.