Enhancing Quantum Entanglement in Bipartite Systems: Leveraging Optimal Control and Physics-Informed Neural Networks

• URL: http://arxiv.org/abs/2403.16321v1
• Date: Sun, 24 Mar 2024 22:59:24 GMT
• Title: Enhancing Quantum Entanglement in Bipartite Systems: Leveraging Optimal Control and Physics-Informed Neural Networks
• Authors: Nahid Binandeh Dehaghani, A. Pedro Aguiar, Rafal Wisniewski,
• Abstract summary: 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.
• Score: 1.4811951486536687
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum entanglement stands at the forefront of quantum information science, heralding new paradigms in quantum communication, computation, and cryptography. This paper introduces a quantum optimal control approach by focusing on entanglement measures rather than targeting predefined maximally entangled states. Leveraging the indirect Pontryagin Minimum Principle, we formulate an optimal control problem centered on maximizing an enhanced lower bound of the entanglement measure within a shortest timeframe in the presence of input constraints. We derive optimality conditions based on Pontryagin's Minimum Principle tailored for a matrix-valued dynamic control system and tackle the resulting boundary value problem through a Physics-Informed Neural Network, which is adept at handling differential matrix equations. The proposed strategy not only refines the process of generating entangled states but also introduces a method with increased sensitivity in detecting entangled states, thereby overcoming the limitations of conventional concurrence estimation.

Related papers

• Quantum Gate Optimization for Rydberg Architectures in the Weak-Coupling Limit [55.05109484230879]
  We demonstrate machine learning assisted design of a two-qubit gate in a Rydberg tweezer system. We generate optimal pulse sequences that implement a CNOT gate with high fidelity. We show that local control of single qubit operations is sufficient for performing quantum computation on a large array of atoms.
  arXiv  Detail & Related papers  (2023-06-14T18:24:51Z)
• Quantum Pontryagin Neural Networks in Gamkrelidze Form Subjected to the Purity of Quantum Channels [1.376408511310322]
  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.
  arXiv  Detail & Related papers  (2023-03-17T23:21:54Z)
• 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)
• Hamiltonian Quantum Generative Adversarial Networks [4.806505912512235]
  We propose Hamiltonian Quantum Generative Adversarial Networks (HQuGANs) to learn to generate unknown input quantum states. We numerically demonstrate the capabilities of the proposed framework to learn various highly entangled many-body quantum states.
  arXiv  Detail & Related papers  (2022-11-04T16:53:55Z)
• Decomposition of Matrix Product States into Shallow Quantum Circuits [62.5210028594015]
  tensor network (TN) algorithms can be mapped to parametrized quantum circuits (PQCs) We propose a new protocol for approximating TN states using realistic quantum circuits. Our results reveal one particular protocol, involving sequential growth and optimization of the quantum circuit, to outperform all other methods.
  arXiv  Detail & Related papers  (2022-09-01T17:08:41Z)
• Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks [68.8204255655161]
  We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms. We consider a network of qubits -- encoded in the states of artificial atoms with no direct coupling -- interacting via a common single-mode driven microwave resonator. We observe high quantum fidelities and resilience to noise, despite the algorithm being trained in the ideal noise-free setting.
  arXiv  Detail & Related papers  (2022-06-29T14:34:00Z)
• Physics-informed neural networks for quantum control [0.0]
  We introduce a computational method for optimal quantum control problems via physics-informed neural networks (PINNs) We apply our methodology to open quantum systems by efficiently solving the state-to-state transfer problem with high probabilities, short-time evolution, and using low-energy consumption controls.
  arXiv  Detail & Related papers  (2022-06-13T16:17:22Z)
• 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)
• Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems [8.920103626492315]
  We look for the optimal control that maximizes quantum Fisher information for "twist and turn" problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced.
  arXiv  Detail & Related papers  (2022-04-30T00:02:57Z)
• 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)
• High Fidelity Quantum State Transfer by Pontryagin Maximum Principle [68.8204255655161]
  We address the problem of maximizing the fidelity in a quantum state transformation process satisfying the Liouville-von Neumann equation. By introducing fidelity as the performance index, we aim at maximizing the similarity of the final state density operator with the one of the desired target state.
  arXiv  Detail & Related papers  (2022-03-07T13:27:26Z)

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.