  We present a low-depth randomised algorithm for the estimation of
entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and
its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified
Pauli-Liouville representation of quantum channels, with Clifford algebra
elements as a basis. We show that this choice of representation leads to a
block-diagonal compound matrix structure of matchgate superoperators which
enables construction of efficient protocols for estimating the fidelity,
achieving a $1/\sqrt{n}$ speedup over protocols of Flammia \& Liu [PRL 106,
230501]. Finally, we offer simple extensions of our protocol which (without
additional overhead) benchmark matchgate circuits intertwined by Clifford
circuits, and circuits composed of exclusively nearest-neighbour $XY(\theta)$
gates or Givens rotations - forming the first known method for direct
benchmarking of matchgate subgroups.
