We describe computational methods for the theoretical study of explicit correlations beyond the mean field in excitons confined in semiconductor quantum dots in terms of the Auxiliary-Field Monte Carlo (AFMC) method. Using AFMC, the many-body problem is formulated as a Feynman path integral at finite temperatures and evaluated to numerical precision. This approach is ideally suited for implementation on high-performance parallel computers. Our strategy is to generate a set of mean-field states via the Hartree-Fock method for use as a basis for the AFMC calculations. We present preliminary results.