The module is a massively parallel implementation of the Trotter-Suzuki approximation to simulate the evolution of quantum systems classically. It relies on interfacing with C++ code with OpenMP for multicore execution, and it can be accelerated by CUDA.

Key features of the Python interface:

  • Simulation of 1D and 2D quantum systems.
  • Cartesian and cylindrical coordinate systems.
  • Fast execution by parallelization: OpenMP and CUDA are supported.
  • Many-body simulations with non-interacting particles.
  • Solving the Gross-Pitaevskii equation (e.g., dark solitons, vortex dynamics in Bose-Einstein Condensates).
  • Imaginary time evolution to approximate the ground state.
  • Stationary and time-dependent external potential.
  • NumPy arrays are supported for efficient data exchange.
  • Multi-platform: Linux, OS X, and Windows are supported.


The original high-performance kernels were developed by Carlos Bederián. The distributed extension was carried out while Peter Wittek was visiting the Department of Computer Applications in Science & Engineering at the Barcelona Supercomputing Center, funded by the “Access to BSC Facilities” project of the HPC-Europe2 programme (contract no. 228398). Generalizing the capabilities of kernels was carried out by Luca Calderaro while visiting the Quantum Information Theory Group at ICFO-The Institute of Photonic Sciences, sponsored by the Erasmus+ programme. Further computational resources were granted by the Spanish Supercomputing Network (FY-2015-2-0023 and FI-2016-3-0042) and the Swedish National Infrastructure for Computing (SNIC 2015/1-162 and 2016/1-320), and a hardware grant by Nvidia. Pietro Massignan has contributed to the project with extensive testing and suggestions of new features.


  1. Bederián, C. & Dente, A. (2011). Boosting quantum evolutions using Trotter-Suzuki algorithms on GPUs. Proceedings of HPCLatAm-11, 4th High-Performance Computing Symposium. PDF
  2. Wittek, P. and Cucchietti, F.M. (2013). A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid CPU-GPU Kernel. Computer Physics Communications, 184, pp. 1165-1171. PDF
  3. Wittek, P. and Calderaro, L. (2015). Extended computational kernels in a massively parallel implementation of the Trotter-Suzuki approximation. Computer Physics Communications, 197, pp. 339-340. PDF