Robust Majorana magic gates via measurements

Abstract

$\pi /8$ phase gates (magic gates or T-gates) are crucial to augment topological systems based on Majorana zero modes to full quantum universality. We present a scheme based on a combination of projective measurements and non-adiabatic evolution that effectively cancels smooth control errors when implementing phase gates in Majorana-based systems. Previous schemes based on adiabatic evolution are susceptible to problems arising from small but finite dynamical phases that are generically present in topologically unprotected gates. A measurement-only approach eliminates dynamical phases. For non-protected gates, however, forced-measurement schemes are no longer effective which leads to low success probabilities of obtaining the right succession of measurement outcomes in a measurement-only implementation. We show how to obtain a viable measurement-based scheme which dramatically increases the success probabilities by evolving the system non-adiabatically with respect to the degenerate subspace in between measurements. We outline practical applications of our scheme in recently proposed quantum computing designs based on Majorana tetrons and hexons.

arXiv comment13 pages, 8 figures. v2: minor updates, added figure of Y-junction

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