  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.
