Large-scale Classical Simulation of Quantum Systems Using the Trotter-Suzuki Decomposition

Many theoretical studies and experimental results rely on the use of numerical analysis for the solution of the Schrödinger equation. Indeed, for nontrivial quantum systems, a complete solution of the dynamics is difficult to achieve analytically. We extended the implementation of a highly optimized solver to simulate the evolution of a wave function on a 2D lattice. We also implemented the imaginary time evolution to approximate the ground state. The dynamics of the system is now described by a Hamiltonian that includes an external potential and a contact interaction term. The algorithm is based on the second-order Trotter-Suzuki approximation and it is implemented on CPU and GPU kernels that run efficiently on a cluster. We proved the accuracy of the code solving the Gross-Pitaevskii equation for a Bose-Einstein condensate and reproducing the experimental results, obtained at NIST, of the soliton dynamics in a cloud of sodium atoms. The code is available under an open source license, and it is exposed as an application program interface and a command-line interface. The code is also accessible in Python and MATLAB. Future development of the code include the extension to a 3D lattice, whereas the actual implementation can already find applications in ultracold atom physics.