Capabilities of object-oriented programming for the construction of quantum-kinetic BBGKY equations of high orders

• URL: http://arxiv.org/abs/2411.09544v1
• Date: Thu, 14 Nov 2024 15:59:11 GMT
• Title: Capabilities of object-oriented programming for the construction of quantum-kinetic BBGKY equations of high orders
• Authors: Ekaterina Tarasevich, Maxim Gladush,
• Abstract summary: We present an object-oriented framework for constructing the equation of motion of the correlation matrix at a given order. It is based on the description and use of classes in the Python programming environment. It is shown that this framework allows one to derive the equations of motion of the fourth-order correlation matrix in less than a minute.
• Score: 0.0
• License:
• Abstract: Theoretical methods based on the density matrix are powerful tools to describe open quantum systems. However, such methods are complicated and intricate to be used analytically. Here we present an object-oriented framework for constructing the equation of motion of the correlation matrix at a given order in the quantum chain of BBGKY hierarchy used to describe the interaction of many-particle systems. The algorithm of machine derivation of equations includes the implementation of the principles of quantum mechanics and operator algebra. It is based on the description and use of classes in the Python programming environment. Class objects correspond to the elements of the equations that are derived: density matrix, correlation matrix, energy operators, commutator and several operators indexing systems. The program contains a special class that allows one to define a statistical ensemble with an infinite number of subsystems. For all classes, methods implementing the actions of the operator algebra are specified. The number of subsystems of the statistical ensemble for the physical problem and the types of subsystems between which pairwise interactions are possible are specified as an input data. It is shown that this framework allows one to derive the equations of motion of the fourth-order correlation matrix in less than a minute.

Related papers

• Hybrid Quantum-Classical Machine Learning with String Diagrams [49.1574468325115]
  This paper develops a formal framework for describing hybrid algorithms in terms of string diagrams. A notable feature of our string diagrams is the use of functor boxes, which correspond to a quantum-classical interfaces.
  arXiv  Detail & Related papers  (2024-07-04T06:37:16Z)
• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics [14.379311972506791]
  We propose quantum methods for solving differential equations based on a gradual improvement of the solution via an iterative process. We benchmark the approach on paradigmatic fluid dynamics problems.
  arXiv  Detail & Related papers  (2024-04-12T17:08:27Z)
• CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebra [62.37017125812101]
  We propose a simple but general framework for large-scale linear algebra problems in machine learning, named CoLA. By combining a linear operator abstraction with compositional dispatch rules, CoLA automatically constructs memory and runtime efficient numerical algorithms. We showcase its efficacy across a broad range of applications, including partial differential equations, Gaussian processes, equivariant model construction, and unsupervised learning.
  arXiv  Detail & Related papers  (2023-09-06T14:59:38Z)
• Vectorization of the density matrix and quantum simulation of the von Neumann equation of time-dependent Hamiltonians [65.268245109828]
  We develop a general framework to linearize the von-Neumann equation rendering it in a suitable form for quantum simulations. We show that one of these linearizations of the von-Neumann equation corresponds to the standard case in which the state vector becomes the column stacked elements of the density matrix. A quantum algorithm to simulate the dynamics of the density matrix is proposed.
  arXiv  Detail & Related papers  (2023-06-14T23:08:51Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• A Quantum Algorithm for Computing All Diagnoses of a Switching Circuit [73.70667578066775]
  Faults are by nature while most man-made systems, and especially computers, work deterministically. This paper provides such a connecting via quantum information theory which is an intuitive approach as quantum physics obeys probability laws.
  arXiv  Detail & Related papers  (2022-09-08T17:55:30Z)
• Quantum algorithms for matrix operations and linear systems of equations [65.62256987706128]
  We propose quantum algorithms for matrix operations using the "Sender-Receiver" model. These quantum protocols can be used as subroutines in other quantum schemes.
  arXiv  Detail & Related papers  (2022-02-10T08:12:20Z)
• A Quantum Computer Amenable Sparse Matrix Equation Solver [0.0]
  We study problems involving the solution of matrix equations, for which there currently exists no efficient, general quantum procedure. We develop a generalization of the Harrow/Hassidim/Lloyd algorithm by providing an alternative unitary for eigenphase estimation. This unitary has the advantage of being well defined for any arbitrary matrix equation, thereby allowing the solution procedure to be directly implemented on quantum hardware.
  arXiv  Detail & Related papers  (2021-12-05T15:42:32Z)
• QOptCraft: A Python package for the design and study of linear optical quantum systems [0.0]
  The package QOptCraft gives a collection of methods to solve some of the most usual problems when designing quantum experiments with linear interferometers. The routines are chosen to avoid usual numerical problems when dealing with the unitary matrices that appear in the description of linear systems.
  arXiv  Detail & Related papers  (2021-08-13T12:05:21Z)
• Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems [17.623937769189364]
  We develop a complete learning theory which establishes strong consistency and optimal nonparametric min-max rates of convergence for the estimators. The numerical algorithm presented to build the estimators is parallelizable, performs well on high-dimensional problems, and is demonstrated on complex dynamical systems.
  arXiv  Detail & Related papers  (2020-10-08T02:07:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.