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Twisted Interferometry

We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other. These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements. In particular, it enables Ising anyons to generate "magic states," which can be used to implement pi/8-phase gates. We consider the possible implementations of such twisted interferometers in quantum Hall systems, 2D p_x + i p_y superconductors, and 2D Majorana heterostructures, and discuss obstacles and challenges associated with implementation.