While the adiabatic exchange of Majorana zero modes (MZMs) enables a nonuniversal set of geometrically protected gates, realizing an experimental implementation of MZM braiding remains challenging. In an alternative proposal, charge-parity measurement of two neighboring MZMs supports braiding by teleportation. Moreover, owing to the lack of definitive evidence of MZMs in semiconducting systems, there have been several simulations of MZMs on noisy intermediate-scale quantum devices which more naturally lend themselves to braiding. In this work, measurement-based braiding about MZM Y junctions is simulated by multiqubit parity measurements of a logical qubit. Logical single-qubit geometric $S^{(†)}$ and entangling two-qubit braiding operations are shown using two-physical-qubit joint measurements alone, while $T^{(†)}$ gates corresponding to a kind of partial-braiding operation require at least one three-qubit joint measurement. These relatively small-scale circuits demonstrate potential applications of both measurement-based geometric gates and a measurement-based demonstration of quantum Hamiltonian simulation.

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• Majorana fermions
• Measurement-based quantum computing
• Quantum simulation