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Computer Physics Communications

QDT — A Matlab toolbox for the simulation of coupled quantum systems and coherent multidimensional spectroscopy

Tristan Kenneweg, Stefan Mueller, Tobias Brixner, Walter Pfeiffer

Published Dec 1, 2023• 6 citations
Publisher

Abstract

We present QDT (“quantum dynamics toolbox”), an open-source Matlab software package that enables users to simulate coupled quantum systems in the subsystem energy eigenbasis using modular functions. QDT requires no user knowledge of operator matrix assembly and automatically performs all necessary operator constructions and Hilbert space expansions. Density matrix propagation is performed by numerically solving the Liouville–von-Neumann equation. In order to simulate dissipation and decoherence effects, the Lindblad formalism is implemented. Furthermore, QDT supplies practical analysis and plotting functions, such as visualization of density matrix and expectation value dynamics, that facilitate the evaluation of simulation results. QDT further provides a module for the simulation of coherent multidimensional spectroscopy. Program Title: QDT — A Quantum Dynamics Toolbox CPC Library link to program files: https://doi.org/10.17632/786vb4rgy3.1 Code Ocean capsule: https://codeocean.com/capsule/4608215 Licensing provisions: MIT Programming language: Matlab R2018a (and above) with parallel computing toolbox (optional) [1] Supplementary material: Available on the QDT website [2] Nature of problem: Coupled quantum systems can be easily set up and discussed as level schemes in the subsystem energy eigenbasis. The simulation of the time evolution of these systems by numerically solving differential equations is not straightforward, however. Simulation code that is written from scratch is time-consuming to create and prone to errors during implementation. Furthermore, if code bases deviate drastically between research groups, reproducibility of results becomes challenging, and communication is hindered. Solution method: QDT addresses the above issues by providing a modular toolbox that contains, among others, elements for the simulation of multi-level quantum systems, quantum harmonic oscillators, their interaction with external electric fields, and dissipation. These elements can be combined by the user to build a specific system of interest. All operators are created and expanded automatically based on a single script file provided by the user. Simulation tasks are automated by a single function call, and parallelized in case of extensive tasks.

DOI
10.1016/j.cpc.2023.109031

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We present QDT (“quantum dynamics toolbox”), an open-source Matlab software package that enables users to simulate coupled quantum systems in the subsystem energy eigenbasis using modular functions. QDT requires no user knowledge of operator matrix assembly and automatically performs all necessary operator constructions and Hilbert space expansions. Density matrix propagation is performed by numerically solving the Liouville–von-Neumann equation. In order to simulate dissipation and decoherence effects, the Lindblad formalism is implemented. Furthermore, QDT supplies practical analysis and plotting functions, such as visualization of density matrix and expectation value dynamics, that facilitate the evaluation of simulation results. QDT further provides a module for the simulation of coherent multidimensional spectroscopy. Program Title: QDT — A Quantum Dynamics Toolbox CPC Library link to program files: https://doi.org/10.17632/786vb4rgy3.1 Code Ocean capsule: https://codeocean.com/capsule/4608215 Licensing provisions: MIT Programming language: Matlab R2018a (and above) with parallel computing toolbox (optional) [1] Supplementary material: Available on the QDT website [2] Nature of problem: Coupled quantum systems can be easily set up and discussed as level schemes in the subsystem energy eigenbasis. The simulation of the time evolution of these systems by numerically solving differential equations is not straightforward, however. Simulation code that is written from scratch is time-consuming to create and prone to errors during implementation. Furthermore, if code bases deviate drastically between research groups, reproducibility of results becomes challenging, and communication is hindered. Solution method: QDT addresses the above issues by providing a modular toolbox that contains, among others, elements for the simulation of multi-level quantum systems, quantum harmonic oscillators, their interaction with external electric fields, and dissipation. These elements can be combined by the user to build a specific system of interest. All operators are created and expanded automatically based on a single script file provided by the user. Simulation tasks are automated by a single function call, and parallelized in case of extensive tasks.
We present qlbm , a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy tailored to the implementation of novel QBMs. The framework interfaces with state-of-the-art quantum software infrastructure to enable efficient simulation and validation pipelines, and leverages novel execution and pre-processing techniques that significantly reduce the computational resources required to develop quantum circuits. We demonstrate the versatility of the software by showcasing multiple QBMs in 2D and 3D with complex boundary conditions, integrated within automated benchmarking utilities. Accompanying the source code are extensive test suites, thorough online documentation resources, analysis tools, visualization methods, and demos that aim to increase the accessibility of QBMs while encouraging reproducibility and collaboration. Program summary Program Title: qlbm CPC Library link to program files: https://doi.org/10.17632/28hkvsg7p2.1 Developer's repository link: https://github.com/QCFD-Lab/qlbm Licensing provisions: MPL-2.0 Programming language: Python3 Supplementary material: The documentation of is available at https://qcfd-lab.github.io/qlbm/ . Nature of problem: The advent of quantum algorithms for computational fluid dynamics brings with it challenges that are new to the established field of computational physics. These challenges include the lack of standardized implementations of the still nascent quantum methods, the intense computational demands of developing and simulating quantum algorithms on hardware available today, and the absence of tools that integrate novel developments into established infrastructure. Because of these current limitations, physicists and mathematicians expend superfluous resources on tasks that more mature computational physics branches have surmounted long ago. Solution method: QLBM is a software package that provides an end-to-end development environment for quantum lattice Boltzmann methods. The modular design and flexible quantum circuit library provide a base for extending and generalizing quantum algorithms. Performance enhancements exploit the paradigm of quantum computing simulations to accelerate the speed at which researchers can verify the validity of their methods. Its integration with state-of-the-art quantum computing software and visualization tools increases the algorithms' accesibility. These features allow QLBM to effectively generate, simulate, and analyze quantum circuits for 2D and 3D computational fluid dynamics problems.
QwaveMPS is an open-source Python library for simulating one-dimensional quantum many-body waveguide systems using matrix product states (MPS). It provides a user-friendly interface for constructing, evolving, and analyzing quantum states and operators, facilitating studies in quantum physics and quantum information with waveguide-QED systems. This approach enables efficient, scalable simulations by focusing computational resources on the most relevant parts of the quantum system. Thus, one can study a wide range of complex dynamical interactions, including time-delayed feedback effects in the non-Markovian regime and deeply nonlinear systems, at a highly reduced computational cost compared to full Hilbert space approaches, making it both practical and convenient to model a variety of open waveguide-QED systems (in Markovian and non-Markovian regimes), treating quantized atoms and quantized photons on an equal footing. The QwaveMPS package automates the waveguide-QED-specific tensor-network operations, including construction of the time-bin evolution operator from physical parameters, the swap network required for delayed interactions, orthogonality-center and truncation management, the matrix-product factorization of NNN-photon Fock-state inputs, and the evaluation of single-time and two-time field observables (such as the second-order quantum correlation function) at chosen points along the waveguide.
We provide a software package for numerical simulations and modeling of complex quantum systems in the presence of dissipation and decoherence for a wider class of problems in the field of quantum technologies. This software is based on the method of quantum trajectories usually used for calculations of the density matrix. An important part of this Toolkit is the universal user interface, which is based on Tool Command Language (TCL) scripting language. It is elaborated in such a manner that the system description and system parameters should not be included in the source code. The core is implemented as a generic set of C++ classes, which can be efficiently reused for modeling of a wide range of photonic systems. The code has been written so as to facilitate optimization of the performance without breaking the object-orientedness of the design. We demonstrate that this software package is very useful for high performance parallel calculations on the Cluster.
We present a general-purpose, open-source software suite, SQUIRREL (Streamlined Quantum Unified Interface for Researching Real-time Excitations with Light), for propagating the time-dependent Schrödinger equation on complex geometries in the presence of time-dependent electric and/or magnetic fields. To handle large systems that can be executed on a conventional desktop computer, the SQUIRREL software suite uses a suite of efficient propagation methods for various quantum dynamics applications, including a new perturbation-based element-dropping algorithm that improves computational performance with minimal loss of accuracy. We analyze the efficacy of these optimizations for Crank-Nicolson, scaled Taylor series approximation, and split-operator propagation methods and discuss the range of their applicability to a variety of quantum dynamics problems. In addition, we provide several examples of time-dependent dynamics calculations and extensive documentation for generating custom geometries, potentials, and time-propagation approaches. Our numerical benchmarks and results demonstrate the versatility of the SQUIRREL software suite for efficiently calculating quantum dynamics in complex nanoscale geometries, particularly in the presence of time-dependent magnetic fields, which have received less attention in previous quantum dynamics studies. Program summary Program Title: SQUIRREL CPC Library link to program files: https://doi.org/10.17632/kfvs5s88sj.1 Licensing provisions: GNU General Public License 3 Programming language: MATLAB Supplementary material: Additional details on calculations with an anisotropic effective mass, determination of timesteps, propagation timings, and element-dropping timings. Nature of problem: The SQUIRREL software suite solves the time-dependent Schrödinger equation for electronic states in the presence of time-dependent electric and/or magnetic fields. The code is well-suited for calculating electron dynamics of complex nanostructures in the effective mass approximation, using various propagation and sparse-matrix techniques to reduce the computational complexity of these problems. The program provides a user-friendly interface for testing these optimizations and generating custom geometries and potentials for systems of interest. Solution method: The SQUIRREL software suite uses Crank-Nicolson, split-operator, Padé approximant, and scaled-Taylor-series-based propagation methods to calculate electron dynamics on a finite-element basis. The code includes a novel perturbation-based element-dropping method, which enables sparse representations of the typically dense finite element Hamiltonian matrix. This capability enables a highly efficient and flexible approach for calculating driven dynamics in quantum systems with complex geometries and time-dependent electric/magnetic fields.
A collection of routines is described which largely automates the process of generating the quantum mechanical equations of motion for problems involving systems with relatively few degrees of freedom. Their use allows the user to adopt a high-level approach to writing simulation programs which concentrates on the physics of the problem, rather than on the details of the solution. Examples are taken from the fields of quantum and atomic optics, but the toolbox is also useful for problems involving quantum information and in teaching quantum mechanics. The toolbox has been implemented using the Matlab programming language, but the ideas may be applied to any other object-oriented language.
A software package for the numerical study of quantum dissipative systems in the field of photonics and quantum optics is developed in a cluster that includes the graphical user interface. Library of C++ classes for numerical simulation of the time evolution of the density matrix, the mean values of different operators (the mean number of photons, the correlation functions of various orders, quadratic mean fluctuations, etc.), the Poincare section, and various quasi-probability distribution functions including the Wigner function in phase space is created. As an application, the results of calculations for a nonlinear oscillator in a strict quantum regime are obtained.