Abstract
The fusion of non-Abelian anyons is a fundamental operation in measurement-only topological quantum computation(1). In one-dimensional topological superconductors (1DTSs)(2-4), fusion amounts to a determination of the shared fermion parity of Majorana zero modes (MZMs). Here we introduce a device architecture(5) that is compatible with future tests of fusion rules. We implement a single-shot interferometric measurement of fermion parity(6-11) in indium arsenide-aluminium heterostructures with a gate-defined superconducting nanowire(12-14). The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of the quantum capacitance of these quantum dots of up to 1 fF. Our quantum-capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio (SNR) of 1 in 3.6 μs 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 1 ms at in-plane magnetic fields of approximately 2 T. We discuss the interpretation of our measurements 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%.