DMRG-based methods for large-scale applications in strongly correlated quantum chemistry

Quantum chemical version of the density matrix renormalization group approach (QC-DMRG) is a method of choice for accurate calculations of strongly correlated molecular systems requiring very large active spaces. It is also one of the methods, which will in the early stage help to benchmark the NISQ devices.

In this talk, I will introduce MOLMPS, the new scalable C++ DMRG implementation, which we have recently developed in order to push the envelope of QC-DMRG calculations. The MOLMPS parallel scheme is based on the in-house MPI global memory library, combines operator and symmetry sector parallelisms, and exploits data locality at maximum. I will present the performance tests with the largest calculation of nitrogenase FeMo cofactor cluster with the active space comprising 113 electrons in 76 orbitals and bond dimension equal to 6000, where we achieved scaling up to approximately 2000 CPU cores.

The DMRG method is very successfull in recovering the strong (static) electron correlation, however, in order to treat the real-life problems with chemical accuracy, one needs some post-DMRG method for capturing the missing dynamical electron correlation. I will discuss two such approaches, which we have recently introduced and tested in connection with DMRG, namely the tailored coupled clusters and the adiabatic connection, which might be used also in the context of variational quantum algorithms.

Last but not least, I would like to sketch how the matrix product state (MPS) wave functions produced by the DMRG algorithm may potentially help as initial guesses of hybrid quantum- classical algorithms.