Extended Software Development Workshop: Quantum Dynamics

If you are interested in attending this event, please visit the CECAM website here.

Workshop Description

Quantum molecular dynamics simulations describe the behavior of matter at the microscopic scale and require the combined effort of theory and computation to achieve an accurate and detailed understanding of the motion of electrons and nuclei in molecular systems. Theory provides the fundamental laws governing the dynamics of quantum systems, i.e., the time-dependent Schroedinger equation or the Liouville-von Neumann equation, whereas numerical techniques offer practical ways of solving those equations for applications. For decades now, theoretical physicists and quantum chemists have been involved in the development of approximations, algorithms, and computer softwares, that together have enabled for example the investigation of photo-activated processes, like exciton transfer in photovoltaic compounds, or of nonequilibrium phenomena, such as the current-driven Joule heating in molecular electronics. The critical challenge ahead is to beat the exponential growth of the numerical cost with the number of degrees of freedom of the studied problem. In this respect, a synergy between theoreticians and computer scientists is becoming more and more beneficial as high-performance computing (HPC) facilities are nowadays widely accessible, and will lead to an optimal exploitation of the computational power available and to the study of molecular systems of increasing complexity.

From a theoretical perspective, the two main classes of approaches to solving the quantum molecular dynamical problem are wavepacket propagation schemes and trajectory-based (or trajectory-driven) methods. The difference between the two categories lies in the way the nuclear degrees of freedom are treated: either fully quantum mechanically or within the (semi)classical approximation. In the first case, basis-function contraction techniques have to be introduced to represent the nuclear wavefunction as soon as the problem exceeds 5 or 6 dimensions. Probably the most successful efforts in this direction have been oriented towards the development of the multi-configuration time-dependent Hartree (MCTDH) method [1]. Other strategies are also continuously proposed, focusing for instance on the identification of procedures to optimize the “space” where the wavefunction information is computed, e.g., by replacing Cartesian grids with Smolyak grids [2], and thus effectively reducing the computational cost of the calculation. In the second case, the nuclear subsystem is approximated classically, or semiclassically. Although leading to a loss of some information, this approximation offers the opportunity to access much larger systems for longer time-scales. Various examples of trajectory-based approaches can be mentioned, ranging from the simplest, yet very effective, trajectory surface hopping and Ehrenfest schemes [3], to the more involved but also more accurate coupled-trajectory mixed quantum-classical (CTMQC) [4] and quantum-classical Liouville equation (QCLE) [5]. At the interface between wavepacket and trajectory schemes, Gaussian-MCTDH [6], variational multi-configuration Gaussian (vMCG) [7], and multiple spawning [8] exploit the support of trajectories to propagate (Gaussian) wavepackets, thus recovering some of the information lost with a purely classical treatment. In the case of trajectory-based techniques, the literature provides a significant number of propositions that aim at recovering some of the quantum-mechanical features of the dynamics via appropriately choosing the initial conditions based on the sampling of a Wigner distribution [9].

From the computational point of view, a large part of the calculation effort is spent to evaluate electronic properties. In fact, the nuclei move under the effect of the electronic subsystem, either “statically” occupying its ground state or “dynamically” switching between excited states. Also, the nuclear dynamics part of a calculation becomes itself a very costly computational task in the case of wavepacket propagation methods. Therefore, algorithms for molecular dynamics simulations are not only required to reproduce realistically the behavior of quantum systems in general cases, but they also have to scale efficiently on parallelized HPC architectures.

The extended software development workshop (ESDW) planned for 2018 has three main objectives: (i) build upon the results of ESDW7 of July 2017 to enrich the library of softwares for trajectory-based propagation schemes; (ii) extend the capabilities of the existing modules by including new functionalities, thus giving access to a broader class of problems that can be tackled; (iii) construct links among the existing and the new modules to transversally connect methods for quantum molecular dynamics, types of modules (HPC/Interface/Functionality), and E-CAM work-packages (WP2 on electronic structure).

The central projects of the proposed ESDW, which are related to the modules that will be provided for the E-CAM library, are:
1. Extension of the ModLib library of model Hamiltonians, especially including high-dimensional models, which are used to test and compare existing propagation schemes, but also to benchmark new methods. The library consists of a set of subroutines that can be included in different codes to generate diabatic/adiabatic potential energy surfaces, and eventually, diabatic and nonadiabatic couplings, necessary for both quantum wavepackets methods and trajectory-based methods.
2. Use of machine-learning techniques to construct analytical forms of potential energy surfaces based on information collected along on-the-fly calculations. The Quantics software [10] provides the platform for performing direct-dynamics propagation employing electronic-structure properties determined at several different levels of theory (HF, DFT, or CASSCF, for example). The sampled nuclear configuration space is employed to build a “library” of potentials, that will be used for generating the potential energy surfaces.
3. Development of an interface for CTMQC. Based on the CTMQC module proposed during the Extended Software Develoment Workshop (ESDW) 7, the interface will allow the evolution of the coupled trajectories according to the CTMQC equations based on electronic-structure information calculated from quantum-chemistry packages, developing a connection between the E-CAM WP2 on electronic structure and WP3 on quantum dynamics. Potentially, CTMQC can be adapted to the Quantics code, since the latter has already been interfaced with several electronic-structure packages. Optimal scaling on HPC architectures is fundamental for maximizing efficiency.
4. Extension of the QCLE module developed during the ESDW7 to high dimensions and general potentials. Two central issues need to be addressed to reach this goal : (i) the use of HPC infrastructures to efficiently parallelize the multi-trajectory implementation, and (ii) the investigation of the stochastic sampling scheme associated with the electronic part of the time evolution. Progress in these areas will aid greatly in the development of this quantum dynamics simulation tool that could be used by the broader community.
5. Development of a module to sample initial conditions for trajectory-based procedures. Based on the PaPIM module proposed during the ESDW7, sampling of initial conditions from a Wigner distribution will be adapted to excited-state problems, overcoming the usual approximation of a molecule pictured as a set of uncoupled harmonic oscillators. Also, an adequate sampling of the ground vibrational nuclear wavefunction would ensure calculations of accurate photoabsorption cross-sections. This topic connects various modules of the E-CAM WP3 since it can be employed for CTMQC, QCLE, and for the surface-hopping functionality (SHZagreb developed during the ESDW7) of Quantics.
6. Optimization of some of the modules for HPC facilities, adopting hybrid OpenMP-MPI parallelization approaches. The main goal here is to be able to exploit different architectures by adapting different kinds of calculations, e.g., classical evolution of trajectories vs. electronic-structure calculations, to the architecture of the computing nodes.

The format and organization described here focuses specifically on the production of new modules. Parallel or additional activities, e.g. transversal workshop on optimization of I/O with electronic structure code and possible exploitation of advanced hardware infrastructures (e.g. booster cluster in Juelich), will also be considered based on input from the community.

[1] H. D. Meyer, U. Manthe, L. S. Cederbaum. Chem. Phys. Lett. 165 (1990) 73.
[2] D. Lauvergant, A. Nauts. Spectrochimica Acta Part A 119 (2014) 18.
[3] J. C. Tully. Faraday Discuss. 110 (1998) 407.
[4] S. K. Min, F. Agostini, I. Tavernelli, E. K. U. Gross. J. Phys. Chem. Lett. 8 (2017) 3048.
[5] R. Kapral. Annu. Rev. Phys. Chem. 57 (2006) 129.
[6] G. A. Worth, I. Burghardt. Chem. Phys. Lett. 368 (2003) 502.
[7] B. Lasorne, M. J. Bearpark, M. A. Robb, G. A. Worth. Chem. Phys. Lett. 432 (2006) 604.
[8] M. Ben-Nun, J. Quenneville, T. J. Martínez. J. Phys. Chem. A 104 (2000) 5161.
[9] J. Beutier, D. Borgis, R. Vuilleumier, S. Bonella. J. Chem. Phys. 141 (2014) 084102.
[10] Quantics. A suite of programs for molecular quantum dynamics. http://stchem.bham.ac.uk/~quantics/doc/
[11] PaPIM. A code for calculation of equilibrated system properties (observables). http://e-cam.readthedocs.io/en/latest/Quantum-Dynamics-Modules/modules/PaPIM/readme.html

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PIM_wd: Module for sampling of the quantum Wigner distribution

 

The PIM_wd module implements the exact quantum Wigner probability distribution function sampling algorithm of the Phase Integration Method [1], and is the main subroutine for the quantum correlation function calculations in the PaPIM code. The module samples the thermal Wigner density using a generalised Monte Carlo scheme for sampling phase space points. The scheme combines the Penalty [2] and Kennedy [3] algorithms to sample noisy probability densities. This is necessary because the estimator of the quantum thermal density is not known analytically but must be computed via a statistical average affected by uncertainty. The sampled points are the basis for the calculation of time-independent and time-dependent system observables.

The module was developed as the main component of the PaPIM code, but also as a standalone subroutine that can be easily implemented in other methods (e.g. the whole family of so-called linearised approximations of quantum dynamics) for which phase space sampling of the exact quantum Wigner probability distribution is required. Because the Phase Integration Method samples a set of independent phase space points, independent instances of the PIM_wd module can be run in parallel in order to parallelise the phase space sampling. In the PaPIM package, the parallelisation is accomplished using MPI, which has proved to provide good scalability of the PaPIM code. The module will also be adapted for HTC capabilities.

Practical application and exploitation of the code

The code has been extensively used for the calculation of the infrared absorption spectrum of CH5+ in the gas phase. [4] This highly flexible molecule is considered a standard benchmark of approximate quantum methods, and has experimental interest, for example, in the context of green chemistry.

This module is part of the modules in deliverable D3.3 which were developed during the E-CAM ESDW7.

 

[1] M. Monteferrante, S. Bonella, G. Ciccotti Quantum dynamical structure factor of liquid neon via a quasiclassical symmetrized method J. Chem. Phys. 138 (2013) 054118

[2] D. M. Ceperley, M. Dewing The penalty method for random walks with uncertain energies J. Chem. Phys. 110 (1999) 9812

[3] A. D. Kennedy, J. Kuti Noise without Noise: A New Monte Carlo Method Phys. Rev. Lett. 54 (1985) 2473

[4] O. Asvany, P. K. P, B. Redlich, I. Hegemann, S. Schlemmer, D. Marx Understanding the infrared spectrum of bare CH5+ Science 309 (2005) 1219

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6 software modules recently delivered in the area of Quantum Dynamics

 

In this report for Deliverable 3.3 of E-CAM [1], 6 software modules in quantum dynamics are presented. Four modules stem from some of the activities performed during the Extended Software Development Workshop (ESDW) held by E-CAM at University College Dublin in July 2017 and originate from input of E-CAM’s academic user base. The other two modules were developed following discussions with our industrial partner IBM, in the framework of E-CAM’s pilot project on Quantum Computing.

Following the order of presentation, the 6 modules are named: LocConQubit, OpenQubit, PaPIM, PIM_wd, PIM_qcf, Openmpbeads. They include code for generation of controlled pulses for qubits and for calculation of quantum time correlation functions and their documentation.

In this report, a short description is written for each module, followed by a link to the respective Merge-Request on theGitLab service of E-CAM. These merge requests contain detailed information about the code development, testing and documentation of the modules. A performance analysis for PaPIM, a package merging the functionality of several modules for quantum dynamics developed in E-CAM and structured to act as a high-performance container for future modules, is also presented. This analysis was performed by the E-CAM software group, in collaboration with the POP Center of Excellence for Computing Applications.

[1] S. Bonella, M. Mališ, A. O’Cais, and L. Liang, “D3.3.: Quantum dynamics e-cam modules ii,” Mar. 2018. [Online]. Available: https://doi.org/10.5281/zenodo.1210077.

Full report available here.

 

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New report published: Identification / Selection of E-CAM Quantum Dynamics Codes for Development

 

As technologies reach atomic length and energy scales, the simulation of quantum effects acquires practical interest beyond basic science in areas ranging from sustainable energy, to medicine, to quantum computing. Brute force simulation of quantum dynamical properties, however, is currently out of reach due to the exponential scaling of its cost with the system size, and the development of approximate methods is an active field that must be coupled with the development of highly effective software to reach the computational capacity necessary to target significant applications. The goal of E-CAM’s Work-package 3 “Quantum Dynamics” (WP3) is to develop software to contribute to this effort by implementing relevant algorithms and fostering the transition from in-house codes to reliable, modular, scalable and well documented community packages.

In this report, we first review current algorithms for the simulation of quantum dynamics, focusing in particular on approximate schemes that achieve satisfactory accuracy with manageable numerical cost and have good potential for massively parallel implementations. We then discuss software packages that make these methods available, focusing in particular on codes that enable to interface quantum dynamical algorithms with ab initio evaluation of the interactions in the system. Finally, we give an overview of the software modules to be developed within WP3 of E-CAM.

Full report available here.

 

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LocConQubit, a module for the construction of controlled pulses on isolated qubit systems using the Local Control Theory

 

The LocConQubit module implements the Local Control Theory[1,2], an algorithm for on-the-fly construction of a time-dependent potential that drives the evolution of a Hamiltonian towards one of its eigenstates. The algorithm is applicable to any Hamiltonian that is separable into a time-dependent and into a time-independent part, where the first part is directly incorporated into the algorithm, while the latter defines the basis of system states from which a designated target state is selected. States with vanishing interaction elements cannot be treated with the aforementioned algorithm. The algorithm is fine-tuned by the user with a single parameter in order to assure physical range of the generated time-dependent potential. This free parameter can be time-dependent while certain constrains in pulse generation can be directly incorporated into the algorithm. The module is accompanied with subroutines for pulse frequency analysis, post-processing, fidelity calculation and visualization of pulses and system evolution. The module is written in Python 3 programming language and is an addition to the open source QuTiP software package. The module uses the OpenMP functionalities available in QuTiP to parallelize the calculation of the pulse fidelity in order to search more efficiently for an optimal control pulse.

Additional module documentation, which includes background information on the Local Control Theory, information about software installation and testing and a link to the source code, can be found in our E-CAM software Library here

Practical application and exploitation of the code

The practical application of this software module is the pilot project with IBM on “Quantum Computing” sustained by an E-CAM postdoctoral researcher at École Polytechnique Fédérale de Lausanne (EPFL).

This module enables to construct more efficient control pulses for superconducting transmon qubits coupled to a single tunable coupler whose energy is controlled with an external electromagnetic pulse. By properly modulating the energy of the tunable coupler with an external control pulse, the coupler operates as a quantum logic gate between coupled qubits. To improve gate performance and thus overall performance of quantum computers, pulses are tailored to make gate operations faster while maintaining at the same time the highest possible fidelity. The Local Control Theory was applied to these systems to generate efficient state preparation pulses which transfer populations completely from one qubit state to the other, as well as pulses for the SWAP gates which completely exchange quantum states between two qubits. A set of pulses capable of transferring populations with a full fidelity to designated target states was generated and, by post-processing this set, an optimal set of pulses for experimental implementation was obtained. This set is currently being tested at IBM. In parallel, capabilities as well as limits of the Local Control theory to manipulate such systems have been investigated in detail. Results of this work are going to be published in two scientific papers. In addition, the current OpenMP parallelization will be upgraded with a more advance parallelization scheme that will enable more efficient utilization of \acs{HPC} resources and an easier implementation of parallelized optimization techniques.

 

[1] B. F. E. Curchod, T. J. Penfold, U. Rothlisberger and I. Tavernelli, Local control theory in trajectory-based nonadiabatic dynamics, Phys. Rev. A, vol. 84, p. 042507, 2011. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.84.042507

[2] V. Engel, C. Meier, and D. J. Tannor, Local Control Theory: Recent Applications to Energy and Particle Transfer Processes in Molecules, John Wiley Sons, Inc., 2009, pp. 29–101. [Online]. Available: http: //dx.doi.org/10.1002/9780470431917.ch2

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Second-Order Differencing Scheme

This module, SodLib, provides exact wavefunction propagation using the second-order differencing (SOD) integrator scheme to solve the time-dependent Schrödinger equation as described by Leforestier et al, J. Comp Phys, 94, 59-80, 1991. Within this scheme the time interval is determined through dividing hbar by the eigenvalue of the Hamiltonian operator with the largest absolute value. This routine has been implemented and tested as an added functionality within the Quantics software package available through CCPForge.

Quantics is a package to study chemical reactions of molecules whose main developer (G. Worth, University College London) is a member of E-CAM’s WP3 – Quantum Dynamics. It incorporates a variety of quantum dynamical methods joined by the fact that the state system is usually described via wavefunctions (containing the quantum analogue of the information given by positions and velocities for classical atoms). It is increasingly used by the computational chemistry community for scientific applications. Work is on-going in E-CAM to improve its scalability (see E-CAM deliverable D7.2 ) and add new functionalities in view of applications to study materials and light harvesting complexes.

Module documentation can be found here, including a link to the source code.

Practical application and exploitation of the code

The module is currently being used in a Phd thesis and the results of this application will provide benchmarks for a model describing proton-transfer in a condensed phase system.

 

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Extended Software Development Workshop: Quantum MD

If you are interested in attending this workshop, please visit the CECAM website bellow.

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ClassMC

Module ClassMC samples the system phase space using the classical Boltzmann distribution function and calculates the time correlation functions from the sampled initial conditions. For more information check the module documentation here.

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