About QDYN

QDYN is a Fortran 95 library and collection of utilities for the simulation of quantum dynamics and optimal control with a focus on both efficiency and precision. Its core features include

  • A rich set of data structures for both closed and open quantum systems
  • Routines for static system analysis (e.g. diagonalization, emission spectra)
  • Propagators for the dynamic equations (Schrödinger equation, master equation) using highly efficient Chebychev and Newton polynomial expansions or the Runge-Kutta method
  • Optimal control using Krotov's method, GRAPE/LBFGS, and gradient-free methods

QDYN has an accompanying Python package that may be used for data processing and for integration into a Python-based workflow.

Applications of QDYN include

  • Simulation of wave packets in molecular dynamics, including both vibrational and rotational degrees of freedom
  • Finding control fields in photo-chemistry, e.g. photo-association of molecules, cooling of vibrational motion
  • Controlling the dynamics of trapped Bose-Einstein condensates
  • Implementation of robust quantum gates at the quantum speed limit on a variety of architectures, e.g. trapped atoms, ions, and superconducting qubits.
  • Typical quantum information tasks such as ion transport

QDYN is undergoing active development and does not yet have a stable release. Please contact us if you are interested in using QDYN.

Data Structures

  • For systems with spatial degrees of freedom (e.g. molecules), QDYN uses spectral methods and grid mapping to achieve an efficient representation
  • For spin-systems, a bit representation may be used
  • For generic quantum systems, operators are stored in sparse matrix formats

QDYN reads and writes all data in a well-defined plain text format, ensuring interoperability with other software packages. The proper use of physical units is enforced throughout.

Propagation Methods

QDYN allows to simulate system dynamics for both closed and open quantum systems to machine precision

  • The time-dependent Schrödinger equation is solved using a Chebychev polynomial expansion
  • For non-Hermitian dynamics, especially the Liouville-von-Neumann equation, a Newton polynomial expansion is used in conjunction with a restarted-Arnoldi (Krylov subspace) method
  • For large open systems, QDYN allows to simulate quantum trajectories using the quantum jump method (MPI parallelized)
  • To simulate the dynamics under strongly varying time-continuous control fields to very high precision, the iterative-time-ordering (ITO) propagator may be used.
  • For non-linear equations of motion, an iterative polynomial propagator may be used
  • Runge-Kutta serves as a fall-back

Optimal Control Methods

QDYN focuses on gradient-based optimal control methods:

  • Krotov's method with both first and second order (the latter supports for non-convex functionals, non-linear equations of motion, non-linear couplings to controls, state-dependent running costs, and spectral constraints)

Furthermore, QDYN can also easily be used for gradient-free optimization methods (Nelder-Mead simplex, CRAB) through simple wrapper scripts, providing an interface to e.g. Python optimization libraries.

QDYN includes several advanced functionals relevant to quantum information processing, e.g. for optimizing towards a general perfect entangler.


Prof. Dr. Christiane Koch
Theoretical Physics
University of Kassel
Heinrich-Plett-Strasse 40
34132 Kassel, Germany

Development Team

QDYN is developed in the group of Prof. Dr. Christiane Koch at the University of Kassel, Germany.

Lead Developers

since 2015 Daniel Basilewitsch
2008 - 2015 Michael Goerz
2007 - 2008 Fabian Krack

See the full list of people that have contributed to QDYN