Mixed-Precision Implementation of the Density Matrix Renormalization Group.

The mixed-precision optimization is an effective emerging technique for quantum chemistry methods to obtain better computational performance and maintain the chemical accuracy. Here, we developed a two-level mixed-precision implementation for the density matrix renormalization group (DMRG) method. This implementation is based on the idea that the DMRG process is an iterative process. Therefore, the first several iteration steps can be executed in single precision. A feasible single-precision DMRG may generate moderate accuracy, and when a few double-precision cleanup sweeps are added, the double-precision accuracy will be recovered. In the double-precision sweeps, we developed a mixed-precision diagonalization method that can run the most time-consuming step in single precision and maintain the double-precision accuracy. By combining these two mixed-precision schemes, we implemented our mixed-precision DMRG method. The benchmark result shows that our mixed-precision implementation achieved a good performance. A speed-up of up to 2.31 is achieved, and the accuracy is preserved within 0.01 kcal/mol.