The Quadratic Assignment Problem formulated as an integer program: \begin{align} \mbox{minimize}\quad & \sum_{i=1}^n\sum_{j=1}^nc_{ij} x_{ij} + \sum_{i=1}^n\sum_{j=1}^n\sum_{k=1}^n\sum_{l=1}^n c_{ijkl}x_{ij}x_{kl}\\ \mbox{subject to}\quad &\sum_{i=1}^n x_{ij} = 1 \quad \forall j=1,\ldots,n,\\ &\sum_{j=1}^n x_{ij} = 1 \quad \forall i=1,\ldots,n,\\ &x_{ij}\in\{0,1\}\quad \forall i,j=1,\ldots,n. \end{align}
A simple and natural linearization: \begin{align} \mbox{minimize}\quad & \sum_{i=1}^n\sum_{j=1}^nc_{ij} x_{ij} + \sum_{i=1}^n\sum_{j=1}^n\sum_{k=1}^n\sum_{l=1}^n c_{ijkl}y_{ijkl}\\ \mbox{subject to}\quad &\sum_{i=1}^n x_{ij} = 1 \quad \forall j=1,\ldots,n,\\ &\sum_{j=1}^n x_{ij} = 1 \quad \forall i=1,\ldots,n,\\ & y_{ijkl} \le x_{ij} \quad \forall i,j,k,l=1,\ldots,n,\\ & x_{ij} + x_{kl} \le 1+y_{ijkl} \quad \forall i,j,k,l=1,\ldots,n,\\ & y_{ijkl} = y_{klij} \quad \forall i,j,k,l=1,\ldots,n,\\ &x_{ij},y_{ijkl}\in\{0,1\}\quad \forall i,j,k,l=1,\ldots,n. \end{align}
My question is: Has this linearization already been considered in the literature? I did not see it in any papers (this one for example).