  Matchgates are a family of parity-preserving two-qubit gates,
nearest-neighbour circuits of which are known to be classically simulable in
polynomial time. In this work, we present a simulation method to classically
simulate an $\boldsymbol{n}$-qubit circuit containing $\boldsymbol{N}$ gates,
$\boldsymbol{m}$ of which are universality-enabling gates and
$\boldsymbol{N-m}$ of which are matchgates, in the setting of single-qubit
Pauli measurements and product state inputs. The universality-enabling gates we
consider include the SWAP, CZ, and CPhase gates. For fixed $\boldsymbol{m}$ as
$\boldsymbol{n} \rightarrow \boldsymbol{\infty}$, the resource cost,
$\boldsymbol{T}$, scales as
$\boldsymbol{\mathcal{O}\left(\left(\frac{en}{m+1}\right)^{2m+2}\right)}$. For
$\boldsymbol{m}$ scaling as a linear function of $\boldsymbol{n}$, however,
$\boldsymbol{T}$ scale as
$\boldsymbol{\mathcal{O}\left(2^{2nH\left(\frac{m+1}{n}\right)}\right)}$, where
$\boldsymbol{H}(\lambda)$ is the binary entropy function.
