  Majorana zero modes (MZMs) promise a platform for topologically protected
fermionic quantum computation. However, creating multiple MZMs and generating
(directly or via measurements) the requisite transformations (e.g., braids)
pose significant challenges. We introduce fermion-parity-based computation
(FPBC): a measurement-based scheme, modeled on Pauli-based computation, that
uses efficient classical processing to virtually increase the number of
available MZMs and which, given magic state inputs, operates without
transformations. FPBC requires all MZM parities to be measurable, but this
conflicts with constraints in proposed MZM hardware. We thus introduce a design
in which all parities are directly measurable and which is hence well suited
for FPBC. While developing FPBC, we identify the "logical braid group" as the
fermionic analog of the Clifford group.
