  Classical realism demands that system properties exist independently of
whether they are measured, while noncontextuality demands that the results of
measurements do not depend on what other measurements are performed in
conjunction with them. The Bell-Kochen-Specker theorem states that
noncontextual realism cannot reproduce the measurement statistics of a single
three-level quantum system (qutrit). Noncontextual realistic models may thus be
tested using a single qutrit without relying on the notion of quantum
entanglement in contrast to Bell inequality tests. It is challenging to refute
such models experimentally, since imperfections may introduce loopholes that
enable a realist interpretation. Here we use a superconducting qutrit with
deterministic, binary-outcome readouts to violate a noncontextuality inequality
while addressing the detection, individual-existence and compatibility
loopholes. This evidence of state-dependent contextuality also demonstrates the
fitness of superconducting quantum circuits for fault-tolerant quantum
computation in surface-code architectures, currently the most promising route
to scalable quantum computing.
