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
- 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.
- 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.
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
- 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
- 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.