Quantum Toolbox in Julia

Yi-Te Huang^1,2,3*, Alberto Mercurio^4,5, Li-Xun Cai^1,2, Vincenzo Savona^4,5, Franco Nori^3,6, Yueh-Nan Chen^1,2,7

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan
²Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan, Taiwan
³RIKEN Center for Quantum Computing, RIKEN, Saitama, Japan
⁴Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
⁵Center for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
⁶Physics Department, The University of Michigan, Michigan, USA
⁷Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

* Presenter:Yi-Te Huang, email:yitehuang.tw@gmail.com

Quantum dynamics describes the time evolution of quantum systems. While the dynamics of closed quantum systems are governed by the Schrödinger equation, open quantum systems require more general theoretical frameworks to accurately capture complex interactions and potential non-Markovian effects arising from their couplings to the surrounding environments. In such cases, analytical solutions are rarely available. To address this, the Quantum Toolbox in Julia project (developed as a sub-project of the QuTiP organization) provides two open-source software packages, QuantumToolbox.jl and HierarchicalEOM.jl, for numerically simulating open quantum system dynamics. Both packages are implemented in Julia programming language and support high-performance computing on CPUs and GPUs. Combining computational efficiency with syntax familiar to QuTiP users, these tools serve as powerful resources for both theoretical research and practical applications in quantum science.

Keywords: open quantum system, quantum simulation, non-Markovian effect, quantum optics, atomic and molecular physics