We study the KPZ equation with a $1+1-$dimensional spacetime white noise,
    started at equilibrium, and give a different proof of the main result of
    \cite{bqs}, i.e., the variance of the solution at time $t$ is of order
    $t^{2/3}$. Instead of using a discrete approximation through the exclusion
    process and the second class particle, we utilize the connection to directed
    polymers in a random environment. Along the way, we show the annealed density
    of the stationary continuum directed polymer equals to the two-point covariance
    function of the stationary stochastic Burgers equation, confirming the physics
    prediction in \cite{MT}.

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