We develop a high-performance simulator for variational quantum eigensolver (VQE), the major innovations include: (1) A differentiable matrix product state (MPS) based VQE simulator that seamlessly integrates MPS into the automatic differentiation framework, which overcomes the exponential memory growth of state-vector simulator and can efficiently calculate gradients with a cost independent of the number of parameters; (2) A dynamic scheme to distribute the gradient calculations to achieve good load balance; (3) A parallel adaptive VQE which integrates our differentiable MPS simulator to further enhance the simulation performance; (4) Study of real chemical systems with convergence to chemical accuracy using our simulator, achieving nearly linearly strong and weak scaling for chemical systems with up to 100 qubits. Our simulator provides an ideal test ground for VQE and paves the way of benchmarking large-scale VQE experiments on near-term quantum computers.

Quantum computational chemistry (QCC) is the use of quantum computers to solve problems in computational quantum chemistry. We develop a high performance variational quantum eigensolver (VQE) simulator for simulating quantum computational chemistry problems on a new Sunway supercomputer. The major innovations include: (1) a Matrix Product State (MPS) based VQE simulator to reduce the amount of memory needed and increase the simulation efficiency; (2) a combination of the Density Matrix Embedding Theory with the MPS-based VQE simulator to further extend the simulation range; (3) A three-level parallelization scheme to scale up to 20 million cores; (4) Usage of the Julia script language as the main programming language, which both makes the programming easier and enables cutting edge performance as native C or Fortran; (5) Study of real chemistry systems based on the VQE simulator, achieving nearly linearly strong and weak scaling. Our simulation demonstrates the power of VQE for large quantum chemistry systems, thus paves the way for large-scale VQE experiments on near-term quantum computers.

The first-principles approach based on density-functional theory (DFT)/density-functional perturbation theory (DFPT) is widely used in calculations of the systems’ ground state energy, response properties (e.g., polarizability, phonon dispersions) and is playing an increasingly important role in chemistry, physics and materials science. For the large-scale calculations, the computation of the density matrix/response density matrix in DFT/DFPT has become the main performance bottleneck. One of the solutions is using the linear scaling method to get the density matrix and response density matrix. Here a massively parallel medium sparse matrix-matrix multiplication algorithm is designed for first-principle calculations and implemented on the new-generation Sunway supercomputer. Experiments show that the proposed method has obvious performance advantages compared to the original parallel version under moderate sparsity. The computing cores scale to 3,900,000 with strong scalability of 77.3$\%$.