Quantum Information Scrambling, Chaos, Sensitivity, and Emergent State Designs

• URL: http://arxiv.org/abs/2409.10182v1
• Date: Mon, 16 Sep 2024 11:20:25 GMT
• Title: Quantum Information Scrambling, Chaos, Sensitivity, and Emergent State Designs
• Authors: Naga Dileep Varikuti,
• Abstract summary: Out-of-time ordered correlators (OTOCs) have emerged as a powerful tool to quantify quantum chaos. OTOCs measure incompatibility between an operator evolved in the Heisenberg picture and an unevolved operator. The last part of the thesis is devoted to the study of the emergence of quantum state designs as a signature of quantum chaos.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding quantum chaos is of profound theoretical interest and carries significant implications for various applications, from condensed matter physics to quantum error correction. Recently, out-of-time ordered correlators (OTOCs) have emerged as a powerful tool to quantify quantum chaos. For a given quantum system, the OTOCs measure incompatibility between an operator evolved in the Heisenberg picture and an unevolved operator. In the first part of this thesis, we employ OTOCs to study the dynamical sensitivity of a perturbed non-Komogorov-Arnold-Moser (non-KAM) system in the quantum limit as the parameter that characterizes the $\textit{resonance}$ condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model that displays stochastic webs in the phase space. The OTOC analysis is followed by a study of quantum Fisher information (QFI) at the resonances and a comparison with the non-resonance cases. We shall show that scaling of the QFI in time is enhanced at the resonances, making the dynamics of the non-KAM systems good candidates for quantum sensing. In the following chapter, we study the OTOCs in a bipartite system of kicked coupled tops with a special focus on the mixed phase space OTOC dynamics. The last part of the thesis is devoted to the study of the emergence of quantum state designs as a signature of quantum chaos and the role of symmetries in this phenomenon. Recently proposed projected ensemble framework utilizes quantum chaos as a resource to construct approximate higher-order state designs. Despite being ubiquitous, the effects of symmetries on the emergence of quantum state designs remain under-explored. We thoroughly investigate this by demonstrating the interplay between symmetries and measurements in constructing approximate state designs. Finally, we outline a few open directions relevant to the current thesis.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Amplification of quantum transfer and quantum ratchet [56.47577824219207]
  We study a model of amplification of quantum transfer and making it directed which we call the quantum ratchet model. The ratchet effect is achieved in the quantum control model with dissipation and sink, where the Hamiltonian depends on vibrations in the energy difference synchronized with transitions between energy levels. Amplitude and frequency of the oscillating vibron together with the dephasing rate are the parameters of the quantum ratchet which determine its efficiency.
  arXiv  Detail & Related papers  (2023-12-31T14:04:43Z)
• Signatures of dissipative quantum chaos [0.0]
  This thesis lays out a generic framework for the study of the universal properties of realistic, chaotic, and dissipative quantum systems. It provides the concrete building blocks of dynamical dissipative evolution constrained by symmetry.
  arXiv  Detail & Related papers  (2023-11-02T18:08:48Z)
• Probing Confinement Through Dynamical Quantum Phase Transitions: From Quantum Spin Models to Lattice Gauge Theories [0.0]
  We show that a change in the type of dynamical quantum phase transitions accompanies the confinement-deconfinement transition. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.
  arXiv  Detail & Related papers  (2023-10-18T18:00:04Z)
• Approximating Quantum Lyapunov Exponents in Quantum Kicked Rotor [0.0]
  We study quantum chaos by focusing on the evolution of initially close states in the dynamics of the Quantum Kicked Rotor (QKR) We propose a novel measure, the Quantum Lyapunov Exponent (QLE), to quantify the degree of chaos in this quantum system, analogous to its classical counterpart.
  arXiv  Detail & Related papers  (2023-07-04T03:47:42Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences [0.0]
  We show the usefulness of multiple quantum coherences for probing equilibrium phase transitions in non-Hermitian systems. Our results have applications to non-Hermitian quantum sensing, quantum thermodynamics, and in the study of the non-Hermitian skin effect.
  arXiv  Detail & Related papers  (2021-09-06T14:30:47Z)
• From geometry to coherent dissipative dynamics in quantum mechanics [68.8204255655161]
  We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation. We describe quantum decays in a 2-level system as coherent and continuous processes.
  arXiv  Detail & Related papers  (2021-07-29T18:27:38Z)
• Revealing higher-order light and matter energy exchanges using quantum trajectories in ultrastrong coupling [0.0]
  We extend the formalism of quantum trajectories to open quantum systems with ultrastrong coupling. We analyze the impact of the chosen unravelling (i.e., how one collects the output field of the system) for the quantum trajectories.
  arXiv  Detail & Related papers  (2021-07-19T11:22:12Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)

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.