PaPIM: A code for Quantum Time Correlation Functions

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PaPIM code is a package to study the (quantum) properties of materials, and in particular time correlation functions, via the so-called mixed quantum-classical methods. In these schemes, quantum evolution is approximated by appropriately combining a set of classical trajectories for the system. Several quantum effects, for example, the possibility to find atoms in classically forbidden regions (tunneling), are reproduced at a manageable fraction of the cost of exact solutions.

The PaPIM module is a high-performance Fortran 90/95 MPI parallelized package for calculating system’s time-dependent observables. The code represents the current optimized assembly of the following modules:

  • PIM_wd and PIM_qcfmodules (described in deliverable D3.3) for exact quantum sampling of the Wigner phase space probability distribution function and the corresponding calculation of specific quantum correlation functions, respectively;
  • ClassMC module (described in D3.1) for Monte Carlo sampling of classical Maxwell-Boltzmann distribution and calculation of corresponding correlation-functions;
  • PotMod module (described in D3.1), a library for model potentials and interfaces to external codes for potential energy calculations used by the sampling modules. This module is currently being enhanced with an interface to couple PaPIM with the CP2K package for electronic structure calculations;
  • AuxMod module (described in D3.1) which provides a tailored set of MPI commands used for code parallelisation as well as input handling subroutines.

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. [1] 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. The calculations performed with PaPIM were used to benchmark both the PIM method for time-correlation functions [2] and to realize the code performance analysis.

Through collaborations the code is also currently employed by several groups in their study of: properties of H2 molecules in clathrates (materials for capture and storage of hydrogen and CO2 in energy applications (University College Dublin); infrared characterisation of molecules, and from it understand the effect that the environment has on their chemical properties, in the atmosphere (Université Pierre et Marie Curie); hydrogen at extreme pressures in the context of geophysical applications (Ecole Normale Supérieure Paris); new potentials to efficiently characterise the chemical reactivity of small water clusters, again with possible applications on the physics of the atmosphere in reactions related to greenhouse effect (University of Bochum).

More description of the code and its systematic tests are reported in the E-CAM deliverable D3.3.

 

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

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


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E-CAM Case Study: Designing control pulses for superconducting qubit systems with local control theory

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Dr. Momir Mališ, École Polytechnique Fédérale de Lausanne, Switzerland

 

Abstract

A quantum logic gate is one of the key components of the quantum computer, and designing an effective quantum universal gate is one of the major goals in the development of quantum computers. We have developed a software based on local control theory to design efficient state preparation control pulses for universal quantum gates which drive full population transfer between qubit states.

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PIM_wd: Module for sampling of the quantum Wigner distribution

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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

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

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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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ClassMC

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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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