Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation

Majorana zero modes (MZMs) could offer a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations for computation (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. Furthermore, given a suitable input state, FPBC operates without the need to perform any transformations such as braids. This could greatly reduce the resource cost of implementing fermionic circuits. However, FPBC requires all MZM parity operators to be measurable, a requirement that conflicts with constraints in previously proposed MZM hardware. We thus introduce a novel design in which all such operators are directly measurable in a single shot, and which is hence well suited to FPBC.