The fusion of non-Abelian anyons or topological defects is a fundamental
operation in measurement-only topological quantum computation. In topological
superconductors, this operation amounts to a determination of the shared
fermion parity of Majorana zero modes. As a step towards this, we implement a
single-shot interferometric measurement of fermion parity in indium
arsenide-aluminum heterostructures with a gate-defined 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 1 fF. Our quantum capacitance measurements
show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7
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. These
results are consistent with a measurement of the fermion parity encoded in a
pair of Majorana zero modes that are separated by approximately 3 μm and
subjected to a low rate of poisoning by non-equilibrium quasiparticles. The
large capacitance shift and long poisoning time enable a parity measurement
error probability of 1
