Noise-resistant Landau-Zener sweeps from geometrical curves

The decoherence of a qubit due to environmental noise is a long-standing problem in quantum information science. Recent work provided a new recipe for designing dynamically corrected gates analytically using a simple geometric formalism. By adapting that formalism, we demonstrate how to design noise-resistant Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is created purely from noise, we demonstrate identity gates and phase gates that are robust against error up to second order. In the more general case where the avoided crossing exists in the absence of noise, we show that robust sweeping protocols are in one-to-one correspondence with curves lying on a sphere that obey certain constraints. We show how to exploit this correspondence to systematically construct noise-resistant Landau-Zener sweeps for generic avoided crossings.