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In this paper, we give a correspondence between the Berezin-Toeplitz and thecomplex Weyl quantizations of the torus $ \mathbb{T}^2$. To achieve this, weuse the correspondence between the Berezin-Toeplitz and the complex Weylquantizations of the complex plane and a relation between the Berezin-Toeplitzquantization of a periodic symbol on the real phase space $\mathbb{R}^2$ andthe Berezin-Toeplitz quantization of a symbol on the torus $ \mathbb{T}^2 $.

Berezin-toeplitz quantization and complex weyl quantization of the torus t${}^2$