Determinant growth conjecture for random symmetric matrices

Let $Q_n$ be the random symmetric matrix whose entries take values $1$ and $-1$, as in the stated model. Determinant growth conjecture. Almost surely,

$$|\det Q_n| = n^{(1/2-o(1))n}.$$

This is the symmetric-matrix analogue of the bound proved by Tao and Vu for the corresponding independent-entry model $A_n$; the conjectured determinant estimate for $Q_n$ remains open.