Realizing Topological States on Quantum Hardware

The fusion of non-Abelian anyons is a fundamental operation in measurement-only topological quantum computation. In one-dimensional topological superconductors, fusion amounts to a determination of the shared fermion parity of Majorana zero modes. Here, we introduce a device architecture that is compatible with future tests of fusion rules. We implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined superconducting nanowire . The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.6 microseconds at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1ms at in-plane magnetic fields of approximately 2T. These measurements are discussed in terms of both topologically trivial and non-trivial origins. The large capacitance shift and long poisoning time enable a parity measurement with an assignment error probability of 1%.