  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.

Quantum Physics