Performance Analysis of CP2K Code for Ab Initio Molecular Dynamics

Using a realistic molecular catalyst system, we conduct scaling studies of ab initio molecular dynamics simulations using the CP2K code on both Intel Xeon CPU and NVIDIA V100 GPU architectures. We explore using process placement and affinity to gain additional performance improvements. We also use statistical methods to understand performance changes in spite of the variability in runtime for each molecular dynamics timestep. We found ideal conditions for CPU runs included at least four MPI ranks per node, bound evenly across each socket, and fully utilizing processing cores with one OpenMP thread per core, no benefit was shown from reserving cores for the system. The CPU-only simulations scaled at 70% or more of the ideal scaling up to 10 compute nodes, after which the returns began to diminish more quickly. Simulations on a single 40-core node with two NVIDIA V100 GPUs for acceleration achieved over 3.7x speedup compared to the fastest single 36-core node CPU-only version, and showed 13% speedup over the fastest time we achieved across five CPU-only nodes.

Correlation-Informed Permutation of Qubits for Reducing Ansatz Depth in VQE

The Variational Quantum Eigensolver (VQE) is a method of choice to solve the electronic structure problem for molecules on near-term gate-based quantum computers. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability. In this work, we propose a novel approach to reduce ansatz circuit depth. Our approach, called PermVQE, adds an additional optimization loop to VQE that permutes qubits in order to solve for the qubit Hamiltonian that minimizes long-range correlations in the ground state. The choice of permutations is based on mutual information, which is a measure of interaction between electrons in spin-orbitals. Encoding strongly interacting spin-orbitals into proximal qubits on a quantum chip naturally reduces the circuit depth needed to prepare the ground state. For representative molecular systems, LiH, H$_2$, (H$_2$)$_2$, H$_4$, and H$_3^+$, we demonstrate for linear qubit connectivity that placing entangled qubits in close proximity leads to shallower depth circuits required to reach a given eigenvalue-eigenvector accuracy. This approach can be extended to any qubit connectivity and can significantly reduce the depth required to reach a desired accuracy in VQE. Moreover, our approach can be applied to other variational quantum algorithms beyond VQE.