  Developing fast, accurate and scalable techniques for quantum state readout
is an active area in semiconductor-based quantum computing. Here, we present
results on dispersive sensing of silicon corner state quantum dots coupled to
lumped-element electrical resonators via the gate. The gate capacitance of the
quantum device is configured in parallel with a superconducting spiral inductor
resulting in resonators with loaded Q-factors in the 400-800 range. For a
resonator operating at 330 MHz, we achieve a charge sensitivity of 7.7
$\mu$e$/\sqrt{\text{Hz}}$ and, when operating at 616 MHz, we get 1.3
$\mu$e$/\sqrt{\text{Hz}}$. We perform a parametric study of the resonator to
reveal its optimal operation points and perform a circuit analysis to determine
the best resonator design. The results place gate-based sensing at par with the
best reported radio-frequency single-electron transistor sensitivities while
providing a fast and compact method for quantum state readout.
