With non-Abelian statistics and nonlocal degrees of freedom, Majorana bound states (MBS) are suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on one-dimensional systems, it requires delicate parameter tuning and its geometric constraints pose significant challenges for the demonstration of non-Abelian statistics. Building on recent experimental advances in planar Josephson junctions (JJs), we propose how to overcome this obstacle in topological JJs and demonstrate non-Abelian statistics with phase or mini-gate control, detected by charge sensing using quantum point contacts. Our proposals, supported by the experiments, would constitute an important milestone towards topological quantum computing.
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