Optimal noise-canceling shortcuts to adiabaticity: application to noisy Majorana-based gates

摘要

Adiabatic braiding of Majorana zero modes can be used for topologicallyprotected quantum information processing. While extremely robust to manyenvironmental perturbations, these systems are vulnerable to noise withhigh-frequency components. Ironically, slower processes needed for adiabaticityallow more noise-induced excitations to accumulate, resulting in anantiadiabatic behavior that limits the precision of Majorana gates if somenoise is present. In a recent publication [Phys. Rev. B 96, 075158 (2017)],fast optimal protocols were proposed as a shortcut for implementing the sameunitary operation as the adiabatic braiding. These shortcuts sacrificetopological protection in the absence of noise but provide performance gainsand remarkable robustness to noise due to the shorter evolution time.Nevertheless, gates optimized for vanishing noise are suboptimal in thepresence of noise. If we know the noise strength beforehand, can we designprotocols optimized for the existing unavoidable noise, which will effectivelycorrect the noise-induced errors? We address this question in the presentpaper. We find such optimal protocols using simulated-annealing Monte Carlosimulations. The numerically found pulse shapes, which we fully characterize,are in agreement with Pontryagin's minimum principle, which allows us toarbitrarily improve the approximate numerical results (due to discretizationand imperfect convergence) and obtain numerically exact optimal protocols. Theprotocols are \textit{bang-bang} (sequence of sudden quenches) for vanishingnoise, but contain continuous segments in the presence of multiplicative noisedue to the nonlinearity of the master equation governing the evolution. We findthat such noise-optimized protocols completely eliminate the above-mentionedantiadiabatic behavior.