  Silicon spin qubits form one of the leading platforms for quantum
computation. As with any qubit implementation, a crucial requirement is the
ability to measure individual quantum states rapidly and with high fidelity. As
the signal from a single electron spin is minute, different spin states are
converted to different charge states. Charge detection so far mostly relied on
external electrometers, which hinders scaling to two-dimensional spin qubit
arrays. As an alternative, gate-based dispersive read-out based on off-chip
lumped element resonators were introduced, but here integration times of 0.2 to
2 ms were required to achieve single-shot read-out. Here we connect an on-chip
superconducting resonant circuit to two of the gates that confine electrons in
a double quantum dot. Measurement of the power transmitted through a feedline
coupled to the resonator probes the charge susceptibility, distinguishing
whether or not an electron can oscillate between the dots in response to the
probe power. With this approach, we achieve a signal-to-noise ratio (SNR) of
about six within an integration time of only 1 $\mu$s. Using Pauli's exclusion
principle for spin-to-charge conversion, we demonstrate single-shot read-out of
a two-electron spin state with an average fidelity of $>$98% in 6 $\mu$s. This
result may form the basis of frequency multiplexed read-out in dense spin qubit
systems without external electrometers, therefore simplifying the system
architecture.
