  The accuracy of phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) can
be systematically improved with better trial states. Using multi-Slater
determinant trial states, ph-AFQMC has the potential to faithfully treat
strongly correlated systems, while balancing the static and dynamical
correlations on an equal footing. This preprint presents an implementation and
application of graphics processing unit-accelerated ph-AFQMC, for multi-Slater
determinant trial wavefunctions (GPU-accelerated MSD-AFQMC), to enable
efficient simulation of large-scale, strongly correlated systems. This approach
allows for nearly-exact computation of ground state energies in multi-reference
systems. Our GPU-accelerated MSD-AFQMC is implemented in the open-source code
\texttt{ipie}, a Python-based AFQMC package [\textit{J. Chem. Theory Comput.},
2022, 19(1): 109-121]. We benchmark the performance of the GPU code on
transition-metal clusters like [Cu$_2$O$_2$]$^{2+}$ and
[Fe$_2$S$_2$(SCH$_3$)]$^{2-}$. The GPU code achieves at least sixfold speedup
in both cases, comparing the timings of a single A100 GPU to that of a 32-CPU
node. For [Fe$_2$S$_2$(SCH$_3$)]$^{2-}$, we demonstrate that our GPU MSD-AFQMC
can recover the dynamical correlation necessary for chemical accuracy with an
MSD trial, despite the large number of determinants required ($>10^5$). Our
work significantly enhances the efficiency of MSD-AFQMC calculations for large,
strongly correlated molecules by utilizing GPUs, offering a promising path for
exploring the electronic structure of transition metal complexes.
