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

Acta Physica Hungarica B) Quantum Electronics

A New Mathematical Tool for an Exact Treatment of Open Quantum Systems Dynamics

Anna Napoli, Stefania Nicolosi, ANTONINO MESSINA

Published Apr 1, 2005• 2 citations
Publisher
DOI
10.1556/aph.23.2005.1-2.12

Related papers

Tensor network methods for non-perturbative dynamics of open quantum systems

Thibaut Lacroix, Adam Burgess, Nicola Lorenzoni +11 more

The description of open quantum system dynamics beyond the perturbative treatment (usually associated with Markovian master equations) is a computationally challenging task due to the unfavorable exponential scaling of memory kernels. Developed over recent decades in the context of quantum information and condensed matter, tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks. This framework enables the formulation of non-perturbative, numerically exact methods for describing the dynamics of open quantum systems to controllable numerical accuracy. In this review, we present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.

quant-pharXiv:2608.09850•Aug 11, 2026•0 citations

Dynamics of Open Quantum Systems

Keith H. Hughes

•Jan 1, 2006•15 citations

HEOM ‐ QUICK2 : A general‐purpose simulator for fermionic many‐body open quantum systems—An update

Daochi Zhang, Lyuzhou Ye, Jiaan Cao +4 more

Abstract Many‐body open quantum systems (OQSs) have a profound impact on various subdisciplines of physics, chemistry, and biology. Thus, the development of a computer program capable of accurately, efficiently, and versatilely simulating many‐body OQSs is highly desirable. In recent years, we have focused on the advancement of numerical algorithms based on the fermionic hierarchical equations of motion (HEOM) theory. Being in‐principle exact, this approach allows for the precise characterization of many‐body correlations, non‐Markovian memory, and non‐equilibrium thermodynamic conditions. These efforts now lead to the establishment of a new computer program, HEOM for QUantum Impurity with a Correlated Kernel, version 2 (HEOM‐QUICK2), which, to the best of our knowledge, is currently the only general‐purpose simulator for fermionic many‐body OQSs. Compared with version 1, the HEOM‐QUICK2 program features more efficient solvers for stationary states, more accurate treatment of non‐Markovian memory, and improved numerical stability for long‐time dissipative dynamics. Integrated with quantum chemistry software, HEOM‐QUICK2 has become a valuable theoretical tool for the precise simulation of realistic many‐body OQSs, particularly the single atomic or molecular junctions. Furthermore, the unprecedented precision achieved by HEOM‐QUICK2 enables accurate simulation of low‐energy spin excitations and coherent spin relaxation. The unique usefulness of HEOM‐QUICK2 is demonstrated through several examples of strongly correlated quantum impurity systems under non‐equilibrium conditions. Thus, the new HEOM‐QUICK2 program offers a powerful and comprehensive tool for studying many‐body OQSs with exotic quantum phenomena and exploring applications in various disciplines. This article is categorized under: Data Science > Computer Algorithms and Programming Software > Simulation Methods Theoretical and Physical Chemistry > Statistical Mechanics

arXiv:2401.01715•Wiley Interdisciplinary Reviews Computational Molecular Science•Jul 1, 2024•19 citations

Dynamics of Open Quantum Systems

Jacek Okołowicz, Marek Płoszajczak, I. Rotter

arXiv:nucl-th/0301094•Springer eBooks•Jan 1, 2004•0 citations

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

Jeremy M. Moix, Jianshu Cao

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

arXiv:1309.2276•The Journal of Chemical Physics•Oct 2, 2013•131 citations

Quantum dynamics and open quantum systems

Dmitry Mozyrsky

•Feb 1, 1999•0 citations
The description of open quantum system dynamics beyond the perturbative treatment (usually associated with Markovian master equations) is a computationally challenging task due to the unfavorable exponential scaling of memory kernels. Developed over recent decades in the context of quantum information and condensed matter, tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks. This framework enables the formulation of non-perturbative, numerically exact methods for describing the dynamics of open quantum systems to controllable numerical accuracy. In this review, we present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.
Abstract Many‐body open quantum systems (OQSs) have a profound impact on various subdisciplines of physics, chemistry, and biology. Thus, the development of a computer program capable of accurately, efficiently, and versatilely simulating many‐body OQSs is highly desirable. In recent years, we have focused on the advancement of numerical algorithms based on the fermionic hierarchical equations of motion (HEOM) theory. Being in‐principle exact, this approach allows for the precise characterization of many‐body correlations, non‐Markovian memory, and non‐equilibrium thermodynamic conditions. These efforts now lead to the establishment of a new computer program, HEOM for QUantum Impurity with a Correlated Kernel, version 2 (HEOM‐QUICK2), which, to the best of our knowledge, is currently the only general‐purpose simulator for fermionic many‐body OQSs. Compared with version 1, the HEOM‐QUICK2 program features more efficient solvers for stationary states, more accurate treatment of non‐Markovian memory, and improved numerical stability for long‐time dissipative dynamics. Integrated with quantum chemistry software, HEOM‐QUICK2 has become a valuable theoretical tool for the precise simulation of realistic many‐body OQSs, particularly the single atomic or molecular junctions. Furthermore, the unprecedented precision achieved by HEOM‐QUICK2 enables accurate simulation of low‐energy spin excitations and coherent spin relaxation. The unique usefulness of HEOM‐QUICK2 is demonstrated through several examples of strongly correlated quantum impurity systems under non‐equilibrium conditions. Thus, the new HEOM‐QUICK2 program offers a powerful and comprehensive tool for studying many‐body OQSs with exotic quantum phenomena and exploring applications in various disciplines. This article is categorized under: Data Science > Computer Algorithms and Programming Software > Simulation Methods Theoretical and Physical Chemistry > Statistical Mechanics
The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.