Quantum Pontryagin Neural Networks in Gamkrelidze Form Subjected to the Purity of Quantum Channels

• URL: http://arxiv.org/abs/2304.02616v3
• Date: Sun, 4 Jun 2023 16:57:56 GMT
• Title: Quantum Pontryagin Neural Networks in Gamkrelidze Form Subjected to the Purity of Quantum Channels
• Authors: Nahid Binandeh Dehaghani, A. Pedro Aguiar, Rafal Wisniewski
• Abstract summary: We investigate a time and energy optimal control problem for open quantum systems. We deal with the state constraints through Gamkrelidze revisited method. We obtain the necessary conditions of optimality through the Pontryagin Minimum Principle.
• Score: 1.376408511310322
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate a time and energy minimization optimal control problem for open quantum systems, whose dynamics is governed through the Lindblad (or Gorini-Kossakowski-Sudarshan-Lindblad) master equation. The dissipation is Markovian time-independent, and the control is governed by the Hamiltonian of a quantum-mechanical system. We are specifically interested to study the purity in a dissipative system constrained by state and control inputs. The idea for solving this problem is by the combination of two following techniques. We deal with the state constraints through Gamkrelidze revisited method, while handling control constraints through the idea of saturation functions and system extensions. This is the first time that quantum purity conservation is formulated in such framework. We obtain the necessary conditions of optimality through the Pontryagin Minimum Principle. Finally, the resulted boundary value problem is solved by a Physics-Informed Neural Network (PINN) approach. The exploited Pontryagin PINN technique is also new in quantum control context. We show that these PINNs play an effective role in learning optimal control actions.

Related papers

• State-Constrained Optimal Control for Coherence Preservation in Multi-Level Open Quantum Systems [1.4811951486536687]
  This paper addresses the optimal control of quantum coherence in multi-level systems, modeled by the Lindblad master equation. We develop an energy minimization framework to control the evolution of a qutrit (three-level) quantum system while preserving coherence between states.
  arXiv  Detail & Related papers  (2024-11-16T16:53:56Z)
• Stochastic optimal control of open quantum systems [0.0]
  We consider the generic problem of state preparation for open quantum systems. The SOC problem requires the solution of the Hamilton-Jacobi-Bellman equation. We derive a class of quantum state preparation problems that can be solved with PI control.
  arXiv  Detail & Related papers  (2024-10-24T10:47:42Z)
• Enhancing Quantum Entanglement in Bipartite Systems: Leveraging Optimal Control and Physics-Informed Neural Networks [1.4811951486536687]
  We formulate an optimal control problem centered on maximizing an enhanced lower bound of the entanglement measure within a shortest timeframe. We derive optimality conditions based on Pontryagin's Minimum Principle tailored for a matrix-valued dynamic control system. The proposed strategy not only refines the process of generating entangled states but also introduces a method with increased sensitivity in detecting entangled states.
  arXiv  Detail & Related papers  (2024-03-24T22:59:24Z)
• Robust Quantum Control in Closed and Open Systems: Theory and Practice [0.0]
  This survey is written for control theorists to provide a review of the current state of quantum control and outline the challenges faced in trying to apply modern robust control to quantum systems. We present issues that arise when applying classical robust control theory to quantum systems, typical methods used by quantum physicists to explore such systems and their robustness, as well as a discussion of open problems to be addressed in the field.
  arXiv  Detail & Related papers  (2023-12-30T18:08:43Z)
• Optimal State Manipulation for a Two-Qubit System Driven by Coherent and Incoherent Controls [77.34726150561087]
  State preparation is important for optimal control of two-qubit quantum systems. We exploit two physically different coherent control and optimize the Hilbert-Schmidt target density matrices.
  arXiv  Detail & Related papers  (2023-04-03T10:22:35Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• An Application of Pontryagin Neural Networks to Solve Optimal Quantum Control Problems [1.5469452301122175]
  Pontryagin maximum principle has proved to play an important role to achieve the maximum fidelity in an optimum time or energy. We formulate a control constrained optimal control problem where we aim to minimize time and also energy subjected to a quantum system satisfying the bilinear Schrodinger equation. We make use of the so-called "qutip" package in python, and the newly developed "tfc" python package.
  arXiv  Detail & Related papers  (2023-02-01T17:48:07Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• A Quantum Optimal Control Problem with State Constrained Preserving Coherence [68.8204255655161]
  We consider a three-level $Lambda$-type atom subjected to Markovian decoherence characterized by non-unital decoherence channels. We formulate the quantum optimal control problem with state constraints where the decoherence level remains within a pre-defined bound.
  arXiv  Detail & Related papers  (2022-03-24T21:31:34Z)
• Einselection from incompatible decoherence channels [62.997667081978825]
  We analyze an open quantum dynamics inspired by CQED experiments with two non-commuting Lindblad operators. We show that Fock states remain the most robust states to decoherence up to a critical coupling.
  arXiv  Detail & Related papers  (2020-01-29T14:15:19Z)

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.