Polynomial-time computability of the lattice theta function

Determine whether there exists a polynomial-time algorithm to compute the lattice theta function Θ(A, d) = Σ_{x∈ℤ^n} exp(2π (x + d)^T A (x + d)) for large n.

Background

To argue that contracting certain quadratic tensor networks is hard when the kernel of the embedding contains many ℤ factors, the authors reduce contraction to computing the lattice theta function Θ(A, d). They note that no polynomial-time algorithm is known for this quantity when the dimension n is large.

Clarifying the computational complexity of Θ(A, d) would have implications for the tractability of contracting broader classes of quadratic tensor networks and for related problems in number theory and computational mathematics.