  Rapid, high-fidelity single-shot readout of quantum states is a ubiquitous
requirement in quantum information technologies, playing a crucial role in
quantum computation, quantum error correction, and fundamental tests of
non-locality. Readout of the spin state of an optically active emitter can be
achieved by driving a spin-preserving optical transition and detecting the
emitted photons. The speed and fidelity of this approach is typically limited
by a combination of low photon collection rates and measurement back-action.
Here, we demonstrate single-shot optical readout of a semiconductor quantum dot
spin state, achieving a readout time of only a few nanoseconds. In our
approach, gated semiconductor quantum dots are embedded in an open microcavity.
The Purcell enhancement generated by the microcavity increases the photon
creation rate from one spin state but not from the other, as well as
efficiently channelling the photons into a well-defined detection mode. We
achieve single-shot readout of an electron spin state in 3 nanoseconds with a
fidelity of (95.2$\pm$0.7)%, and observe quantum jumps using repeated
single-shot measurements. Owing to the speed of our readout, errors resulting
from measurement-induced back-action have minimal impact. Our work reduces the
spin readout-time to values well below both the achievable spin relaxation and
dephasing times in semiconductor quantum dots, opening up new possibilities for
their use in quantum technologies.
