  In this work, in the framework of dynamical system analysis, we focus on the
study of the accelerated expansion of the Universe of $f(Q)$ gravity theory
where $Q$ be the non-metricity that describes the gravitational interaction. We
consider the linear form of $f(Q)$ gravity i.e. $f(Q)=-\alpha_{1}Q-\alpha_{2}$
where $\alpha_{1}$ and $\alpha_{2}$ are constants. We consider an interaction
between dark matter (DM) and dark energy (DE) in $f(Q)$ gravity. To reduce the
modified Friedmann equations to an autonomous system of first-order ordinary
differential equations, we introduce some dimensionless new variables. The
nature of the critical points are discussed by finding the eigenvalues of the
Jacobian matrix. We get six critical points for interacting DE model. We also
analyze the density parameter, equation of state (EoS) parameter and
deceleration parameter and draw their plots and we conclude that for some
suitable range of the parameters $\lambda$ and $\alpha$, the value of the
deceleration parameter is $q=-1$ which shows that the expansion of Universe is
accelerating and the value of EoS parameter is $\omega_{\phi}=-1$ which shows
that the model is $\Lambda$CDM model. Finally, we discussed the classical as
well as quantum stability of the model.
