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We present a polynomial-time randomized algorithm for estimating thepermanent of an arbitrary $M \times M$ real matrix $A$ up to an additive error.We do this by viewing the permanent of $A$ as the expectation of a product of acentered joint Gaussian random variables whose covariance matrix we call theGaussian embedding of $A$. The algorithm outputs the empirical mean $S_{N}$ ofthis product after sampling from this multivariate distribution $N$ times. Inparticular, after sampling $N$ samples, our algorithm runs in time $O(MN)$ withfailure probability \begin{equation*}  P(|S_{N}-\text{perm}(A)| > t) \leq \frac{3^{M}}{t^{2}N}\alpha^{2M}\end{equation*} for $\alpha \geq \|A \|$.

A polynomial time additive estimate of the permanent using Gaussian fields