Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Contemporary Physics (Armenian Academy of Sciences)

Parallel computations of dissipative quantum systems: A nonlinear oscillator in a strict quantum regime

A. R. Shahinyan, T. V. Gevorgyan

Published Apr 28, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.3103/s1068337213030031

Related papers

Software for numerical simulations in the field of quantum technologies based on parallel programming

Hayk H. Adamyan, N. H. Adamyan, Narine Gevorgyan +2 more

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.

Physics of Particles and Nuclei Letters•May 1, 2008•6 citations

Cloud Service for Numerical Calculations and Visualizations of Photonic Dissipative Systems

Hayk Grigoryan, Hrachya V. Astsatryan, T. V. Gevorgyan +1 more

Abstract Nowadays quantum physics is crucial for several scientific applications, where it is no longer possible to neglect the environmental interaction, like dissipation and decoherence. In these cases, the quantum systems are usually treated as open systems and their time-evolution is described by a density matrix in frames of the master equation, instead of the Hilbert-space vector and the Schrodinger equation. The visualization of such quantum systems allows users to calculate and study the sensitivity of the parameters, like excitation photon numbers or photonnumber distribution functions or Wigner functions. In this paper, a cloud service for numerical calculations and visualization of photonic dissipative systems is presented, which enables numerical simulations and visualizations of a wide variety of Hamiltonians, including those with arbitrary time-dependences widely used in many physics applications. The service allows creating graphics and charts for interacting complex systems and simulating their time evolution with many available timeevolution drivers.

Cybernetics and Information Technologies•Dec 20, 2017•2 citations

1 Dissipative Chaos in Quantum Distributions

T. V. Gevorgyan, Suren B. Manvelyan

We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions.For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field.This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes.Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories.Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory.The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.

•Aug 14, 2016•2 citations

DISSIPATIVE CHAOS IN QUANTUM DISTRIBUTIONS

T. V. GEVORGYAN, S. B. MANVELYAN, A. R. SHAHINYAN +1 more

We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincare section and quantum Poincare section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.

arXiv:1101.5750•Jun 1, 2010•4 citations

Phase-space dynamics of a quantum dissipative Kerr nonlinear oscillator

Karjula, Matias

Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.

•Oct 24, 2025•0 citations

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

Tristan Kenneweg, Stefan Mueller, Tobias Brixner +1 more

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.

Computer Physics Communications•Dec 1, 2023•6 citations
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.
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.
Abstract Nowadays quantum physics is crucial for several scientific applications, where it is no longer possible to neglect the environmental interaction, like dissipation and decoherence. In these cases, the quantum systems are usually treated as open systems and their time-evolution is described by a density matrix in frames of the master equation, instead of the Hilbert-space vector and the Schrodinger equation. The visualization of such quantum systems allows users to calculate and study the sensitivity of the parameters, like excitation photon numbers or photonnumber distribution functions or Wigner functions. In this paper, a cloud service for numerical calculations and visualization of photonic dissipative systems is presented, which enables numerical simulations and visualizations of a wide variety of Hamiltonians, including those with arbitrary time-dependences widely used in many physics applications. The service allows creating graphics and charts for interacting complex systems and simulating their time evolution with many available timeevolution drivers.
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions.For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field.This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes.Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories.Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincaré section and quantum Poincaré section calculated on a single quantum trajectory.The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.
We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincare section and quantum Poincare section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.
Parametrically driven Kerr nonlinear quantum oscillator plays a central role in quantum optics, superconducting circuits, and in engineered light-matter interactions. For the development of future quantum technologies, it is crucial to understand the behavior of this quantum system under realistic dissipative conditions. The objective of this thesis is to investigate the phase-space dynamics of a dissipative Kerr nonlinear oscillator under different driving regimes and corresponding dissipation channels, with a particular focus on the emergence of nonclassical features in phase space. The aim is also to understand how nonlinearity and different driving mechanisms influence quantum properties such as coherence, nonclassicality, and phase-space structure. The analysis was carried out using the Wigner phase-space formalism and numerical simulations of the Lindblad master equation. The results show that in the case of finite nonlinearity the coherence time is prolonged compared to the harmonic case. In the single photon regime, the interplay between the photon drive and nonlinearity can lead to coherence revivals after which the system relaxes into a squeezed steady state. In the two photon and dissipation regime, the system exhibits parity-protected dynamics, leading to very long coherence times.
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.