# Quantum Dynamics Modules¶

## Introduction¶

This is a collection of the modules that have been created by the E-CAM community within the area of Quantum Dynamics. This documentation is created using ReStructured Text and the git repository for the documentation. Source files can be found at https://gitlab.e-cam2020.eu/e-cam/E-CAM-Library which are open to contributions from E-CAM members.

In the context of E-CAM, the definition of a software module is any piece of software that could be of use to the E-CAM community and that encapsulates some additional functionality, enhanced performance or improved usability for people performing computational simulations in the domain areas of interest to the project.

This definition is deliberately broader than the traditional concept of a module as defined in the semantics of most high-level programming languages and is intended to capture internal workflow scripts, analysis tools and test suites as well as traditional subroutines and functions. Because such E-CAM modules will form a heterogeneous collection we prefer to refer to this as an E-CAM software repository rather than a library (since the word library carries a particular meaning in the programming world). The modules do however share with the traditional computer science definition the concept of hiding the internal workings of a module behind simple and well-defined interfaces. It is probable that in many cases the modules will result from the abstraction and refactoring of useful ideas from existing codes rather than being written entirely de novo.

Perhaps more important than exactly what a module is, is how it is written and used. A final E-CAM module adheres to current best-practice programming style conventions, is well documented and comes with either regression or unit tests (and any necessary associated data). E-CAM modules should be written in such a way that they can potentially take advantage of anticipated hardware developments in the near future (this is one of the training objectives of E-CAM).

## Objectives of E-CAM WP3 Quantum Dynamics¶

Software development in quantum dynamics has so far been less systematic than in other fields of modelling, such as classical molecular dynamics or electronic structure. Although some packages have been developed to implement specific methods, e.g. Quantics for wave packet dynamics, or subroutines added to electronic structure packages, e.g. Surface Hopping and Ehrenfest in CPMD, these efforts are not the standard.

One of the goals of E-CAM’s WP3 is then to provide an environment to stimulate the transition from in-house codes, often developed and used by single groups, to the development of modular, well documented community-based software packages capable of multiple functionalities and adopting a common set of standards and benchmarks.

To foster this development, we have initiated five parallel activities:

- Creating software for benchmarking and testing based on exact integration schemes for low dimensional systems and standard potentials.
- Creating an environment to transform in-house software to modules that adhere to the E-CAM best practices.
- Disseminating this initiative to attract coding efforts from leading groups in the field to the E-CAM repository.
- Interact with industrial partners to enrich our repository with software targeted at their needs.
- Training young code developers.

## Pilot Projects¶

One of primary activity of E-CAM is to engage with pilot projects with industrial partners. These projects are conceived together with the partner and typically are to facilitate or improve the scope of computational simulation within the partner. The related code development for the pilot projects are open source (where the licence of the underlying software allows this) and are described in the modules associated with the pilot projects.

The pilot project of the WP3 in collaboration with IBM is related to quantum computing and improvements of the quantum computer technology. One of our main topic was development of software for construction of control pulses necessary for operating quantum logical gates between qubits in a universal quantum computer using the Local Control Theory. [Curc] More information can be found on the pilot project web site. Below are listed the pilot project modules created so far:

**LocConQubit** is a code for the construction of controlled pulses on isolated qubit systems using the Local Control Theory.

**OpenQubit** is an extension to the LocConQubit code for the construction of controlled pulses in a more realistic environment with
dissipating effects.

## Extended Software Development Workshops¶

### ESDW Maison de la Simulation (Paris 2016)¶

The first Quantum Dynamics ESDW was held in June-July 2016 at the Maison de la Simulation near Paris. 10 students and 6 tutors, including Dr. Ivano Tavernelli representing the industrial partner of the WP3, IBM, worked to develop software modules in the following areas:

- Exact quantum propagation methods for low dimensional systems to be used to provide benchmarks for approximate schemes
- Development of a library of single and multi surface potentials for benchmark systems
- Calculation of approximate quantum time correlation functions

Work was performed by teams of 2-4 students, assisted by the senior participants and by E-CAM’s Software Manager, Dr. Alan O’Cais, and the Software Developer associated to WP3, Dr. Liang Liang.

In addition to the software development activities, the Workshop enjoyed lively scientific discussions centered on presentations made by the students and the senior participants. The on-line E-CAM tools for software development, including the Git repository, and tools for the documentation (Doxygen) and performance analysis were presented by E-CAM staff members and participants were instructed on their use via tutorials. The program was further enriched by the interactions with experts on software and hardware development working at Maison de la Simulation who gave talks on topics such as architectures and programming paradigms and the use of advanced visualization tools such as the Image wall hosted by the Maison de la Simulation.

### ESDW University College Dublin (2017)¶

The second Quantum Dynamics ESDW was held in July 2017 (first part) and March 2018 (wrap up meeting) at University College Dublin. 21 participants, including the representative of WP3’s current industrial partner IBM, worked to develop and upload on the E-CAM repositories software modules in the following areas:

- Calculation of approximate quantum time correlation functions via the PaPIM code;
- Mixed quantum-classical algorithms, with specific reference to Surface Hopping and Wigner-Liouville methods;
- Implementation of the factorization scheme for quantum dynamics in CPMD;
- Interfacing of quantum codes with electronic structure codes;
- Grid based exact propagation schemes;
- Design and optimization of qubit control pulses.

Teams of coders assisted by senior tutors, E-CAM’s Software Manager, Dr. Alan O’Cais, and WP3 Software Developer, Dr. Liang Liang, performed the work. Specific discussions on optimal parallelization strategies for the E-CAM’s quantum dynamical codes (PaPIM and Quantics) were also initiated and implemented. The coding work was accompanied by scientific presentations on the themes of the workshops and by the instruction from E-CAM personnel on the CoE’s tools for software production, testing, documentation and maintaining. The participants benefitted also from the proximity of software and hardware experts from the ICHEC supercomputing center that offered, in particular, a set of lectures and tutorials on OpenMP parallelization.

## List of available Modules¶

Below are listed all the modules from the E-CAM ESDWs in Quantum Dynamic developed up-to-date:

The **CTMQC** module allows to simulate excited-state dynamics in model systems of one to three spatial (nuclear) dimensions,
with an arbitrary number of electronic states. The algorithm is based on the quantum-classical approximation of the equations
of motion derived in the framework of the exact factorization of the electron-nuclear wavefunction.
In practice, trajectories are used to mimic the nuclear evolution, that is, in turn, coupled to the quantum evolution of the electronic degrees of freedom.

The **SinglePath** module uses combined quantum and classical descriptions of the dynamics to compute quantum rate processes in condensed phase systems.
The main purpose of this module is to act as the core of additional software modules aimed at addressing important issues such as improving the speed of convergence of
estimates using correlated sampling, and much more realistic treatment of the classical bath, and connecting to other problems such as constant pH simulation
through an effective Hamiltonian.

The **PhysConst** enables the use of physical constants and the correct isotopic masses.

The **QuantumModelLib** use potential energy surfaces extracted from the literature and can be linked to quantum dynamics codes.

### PaPIM¶

PaPIM is a code for calculation of equilibrated system properties (observables). Some properties can be directly obtained from the distribution function of the system, while properties that depends on the exact dynamics of the system, such as the structure factor, [Mon2] infrared spectrum [Beu] or reaction rates, can be obtained from the evolution of appropriate time correlation functions. PaPIM samples either the quantum (Wigner) or classical (Boltzmann) density functions and computes approximate quantum and classical correlation functions. The code is highly parallelized and suitable for use on large HPC machines. The code’s modular structure enables an easy update/change of any of its modules. Furthermore the coded functionalities can be used independently of each other. The code is specifically design with simplicity and readability in mind to enable any user to easily implement its own functionalities. The code has been extensively used for the calculation of the infrared spectrum of the cation in gas phase, while recently new calculations on the water dimer, and protonated water dimer systems were started.

**PaPIM** is the current version of the code, including all available functionalities.

The following modules make up the PaPIM code and can be used as stand-alone software libraries for e.g. sampling of the Wigner distribution, sampling of the classical Boltzmann distribution, or building MPI parallelized Fortran codes. Such libraries are rarely available to the community in a Fortran program format. Some of the functionalities within the code are specifically designed for computation of infrared spectra, and serve as a template for the user to implement its own functionalities.

**PIM_wd** samples, via the Phase Integration Method, [Mon1] the system’s quantum Wigner density function.
The function is given in the phase-space representation and is the basis for any further calculation of system’s quantum observables.

**PIM_qcf** is a library of quantum correlation functions for computing system’s time-dependent properties.

**PIM_qtb** implements various classical and semi-classical methods based on Langevin dynamics (classical Langevin dynamics, Quantum Thermal Bath (QTB) and two variants of adaptive QTB (adQTB-r and adQTB-f). The generated trajectories can be used to sample initial conditions for intramolecular vibrational-energy redistribution (IVR) dynamics.

**ClassMC** samples, via Metropolis Monte Carlo algorithm, the system’s classical Boltzmann distribution function and calculates
the classical time-dependent correlation functions from the sampled phase space.
Results obtained from classical sampling can be used to assess the relevance of quantum effects for a given system.

**PotMod** is a library of potential energy functions and interfaces for external potential energy calculation codes.
Currently available in the library are the harmonic and Morse potentials (different molecular systems can be simulated depending on parameters
provided by the user); empirical potential of the ground state of based on high level
electronic structure calculations [ZJin]; and the call to the ab initio CP2K code using the **PaPIM-CP2K_Interface** module.

**PaPIM-CP2K_Interface** module links the PaPIM code with the CP2K program package
as an internal library for calculation of system’s electronic structure properties.

**AuxMod** is a library of subroutines which enables any user to easily construct its own Fortran input parser.
It also contains a library of adapted MPI subroutines for easier programming of Fortran MPI parallel codes.

**Openmpbeads** is a patch to the PaPIM code which enables parallelization of the sampling of the
polymer chains within the PIM algorithm, improving efficiency in sampling of the Wigner density.

### Quantics¶

Quantics is suite of programs for molecular quantum dynamics simulations. The package is able to set up and propagate a wavepacket using the MCTDH method [Beck]. Numerically exact propagation is also possible for small systems using a variety of standard integration schemes [Lefo], as is the solution of the time-independent Schrödinger equation using Lanczos diagonalisation. The program can also be used to generate a ground state wavefunction using energy relaxation (i.e. propagation in imaginary time) and with the “improved relaxation” it is even possible to generate (low lying) excited states. Within the Quantics package there are also programs to propagate density operators (by solving the Liouville-von Neumann equation for open or closed system) [Mey], a program for fitting complicated multi-dimensional potential energy function, programs for determining bound or resonance energies by filter-diagonalisation, parameters of a vibronic coupling Hamiltonian, and many more. Recent developments include the use of Gaussian wavepacket based methods (G-MCTDH) and interfaces to quantum chemistry programs such as Gaussian and Molpro allow direct dynamics calculations using the vMCG method [Ric]. The following modules are extension of Quantics functionalities developed at E-CAM Extended Software Development Workshops.

The **SodLib** module provides exact wavefunction propagation using the second-order differencing (SOD) integrator
scheme to solve the time-dependent Schrödinger equation. This routine has been implemented and tested as an added
functionality within the Quantics quantum dynamics package.

The **ChebLib** module implements the Chebyshev integration scheme for exact wavefunction propagation on the grid. This
routine has been implemented and tested as an added functionality within the Quantics quantum dynamics package.

The **Quantics-QChem-Interface** is an interface between Quantics and QChem. The DFT algorithm
implemented in QChem can be used to provide electronic structure information for direct dynamics simulations using the Quantics program package.

The **Zagreb_sh** module is an interface between between Quantics package and the Tully’s surface hoping code provided by the group of Nadja Doslic in Zagreb.

The **Quantics_openmp** module is an initial effort at OpenMP parallelisation improvements to Quantics.

## References¶

[Curc] | B. F. E. Curchod, T. J. Penfold, U. Rothlisberger, I. Tavernelli Phys. Rev. A
84 (2012) 042507 DOI: 10.1103/PhysRevA.84.042507 |

[Mon1] | M. Monteferrante, S. Bonella, G. Ciccotti Mol. Phys. 109 (2011) 3015 DOI: 10.1080/00268976.2011.619506 |

[Mon2] | M. Monteferrante, S. Bonella, G. Ciccotti J. Chem. Phys. 138 (2013) 054118 DOI: 10.1063/1.4789760 |

[Beu] | J. Beutier, M. Monteferrante, S. Bonella, R. Vuilleumier, G. Ciccotti Mol. Sim. 40 (2014) 196 DOI:
10.1080/08927022.2013.843776 |

[ZJin] | Z. Jin, B. Braams, J. Bowman J. Phys. Chem. A 110 (2006) 1569 DOI: 10.1021/jp053848o |

[Beck] | M. Beck, A. Jäckle, G.A. Worth, and H.-D. Meyer Phys. Rep. 324 (2000) 1–106
DOI: 10.1016/S0370-1573(99)00047-2 |

[Lefo] | C. Leforestier, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg, A. Hammerich,
G. Jolicard, W. Karrlein, H.-D. Meyer, N. Lipkin, O. Roncero, R. Kosloff J. Comp. Phys. 94 (1991) 59
DOI: 10.1016/0021-9991(91)90137-A |

[Mey] | H.-D. Meyer, G. A. Worth Theor. Chem. Acc. 109 (2003) 251 DOI: 10.1007/s00214-003-0439-1 |

[Ric] | G. W. Richings, I. Polyak, K. E. Spinlove, G. A. Worth, I. Burghardt, B. Lasorne
Int. Rev. Phys. Chem. 34 (2015) 269 DOI: 10.1080/0144235X.2015.1051354 |