Approximating Quantum Lyapunov Exponents in Quantum Kicked Rotor
- URL: http://arxiv.org/abs/2307.01461v2
- Date: Sun, 29 Oct 2023 18:51:21 GMT
- Title: Approximating Quantum Lyapunov Exponents in Quantum Kicked Rotor
- Authors: Varsha Gupta
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, 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.
We begin by modeling the momentum space and then the QLE is computed through
analyzing the fidelity between evolving states, offering insights into the
quantum chaotic behavior. Furthermore, we extend our investigations to various
initial states: localized, uniform, spreading, contracting and oscillating in
momentum space. Our results unveil a diverse range of dynamical behaviors,
highlighting the complex nature of quantum chaos. Finally, we propose an
innovative optimization framework to represent a complex state as a
superposition of the aforementioned states, which has potential implications
for visualizing and understanding the dynamics of multifaceted quantum systems.
Related papers
- Quantum ergodicity and scrambling in quantum annealers [0.0]
We show that the unitary evolution operator describing the complete dynamics of quantum annealers is typically highly quantum chaotic.
We observe that the Heisenberg dynamics of a quantum annealer leads to extensive operator spreading, a hallmark of quantum information scrambling.
arXiv Detail & Related papers (2024-11-19T16:34:35Z) - Quantum coarsening and collective dynamics on a programmable quantum simulator [27.84599956781646]
We experimentally study collective dynamics across a (2+1)D Ising quantum phase transition.
By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries.
We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode.
arXiv Detail & Related papers (2024-07-03T16:29:12Z) - 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) - Quantum and classical coarsening and their interplay with the
Kibble-Zurek mechanism [0.0]
Out-of-equilibrium dynamics of a quantum system driven across a quantum phase transition is an important problem.
We develop a universal description of such coarsening dynamics and their interplay with the Kibble-Zurek mechanism.
We highlight how such coarsening dynamics can be directly studied in today's "synthetic" quantum many-body systems.
arXiv Detail & Related papers (2024-01-26T19:00:00Z) - Effective Description of the Quantum Damped Harmonic Oscillator:
Revisiting the Bateman Dual System [0.3495246564946556]
We present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics.
The significance of our study lies in its potential to serve as a foundational basis for the effective description of open quantum systems.
arXiv Detail & Related papers (2023-09-06T03:53:09Z) - 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) - Unraveling the Mystery of Quantum Measurement with A New Space-Time Approach to Relativistic Quantum Mechanics [9.116661570248171]
Quantum measurement is a fundamental concept in the field of quantum mechanics.
Despite its significance, four fundamental issues continue to pose significant challenges to the broader application of quantum measurement.
We employ a new space-time approach to relativistic quantum mechanics to address these issues systematically.
arXiv Detail & Related papers (2023-06-01T13:25:08Z) - 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) - 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) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z) - 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.