Symmetric Bernoulli determinant conjecture

Let $Q_n$ be the random symmetric matrix whose upper-diagonal entries are independent Bernoulli random variables. Symmetric determinant conjecture. Almost surely,

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

This is the symmetric analogue of the determinant estimate for nonsymmetric Bernoulli matrices. The source notes that nonsingularity had recently been proved, but the sharp determinant asymptotic remained open there.