Lecture Notes on Information Scrambling, Quantum Chaos, and Haar-Random States

• URL: http://arxiv.org/abs/2511.14397v1
• Date: Tue, 18 Nov 2025 12:02:37 GMT
• Title: Lecture Notes on Information Scrambling, Quantum Chaos, and Haar-Random States
• Authors: Marcin Płodzień,
• Abstract summary: Information scrambling is central to modern quantum statistical physics and quantum chaos.<n>Lecture notes provide an introduction to information scrambling from both static and dynamical perspectives.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information scrambling from both static and dynamical perspectives. The spectral properties of reduced density matrices arising from Haar-random states are developed through the geometry of the unitary group and the universal results of random matrix theory. This geometric framework yields universal, model-independent predictions for entanglement and spectral statistics, capturing generic features of quantum chaos without reference to microscopic details. Dynamical diagnostics such as the spectral form factor and out-of-time-ordered correlators further reveal the onset of chaos in time-dependent evolution. The notes are aimed at advanced undergraduate and graduate students in physics, mathematics, and computer science who are interested in the connections between quantum chaos, information dynamics, and quantum computing. Concepts such as entanglement growth, Haar randomness, random-matrix statistics, and unitary t-designs are introduced through their realization in random quantum circuits and circuit complexity. The same mathematical framework also underpins modern quantum-device benchmarking, where approximate unitary designs and random circuits translate geometric ideas into quantitative tools for assessing fidelity, noise, and scrambling efficiency in real quantum processors.

Related papers

• Noisy Monitored Quantum Circuits [2.903954725384182]
  Noisy monitored quantum circuits have emerged as a versatile and unifying framework connecting quantum many-body physics, quantum information, and quantum computation.<n>A central theme is the mapping to classical statistical models, which reveals how quantum noise reshapes dominant spin configurations.<n>We highlight a broad range of constructions and applications inspired by noisy monitored circuits, spanning variational quantum algorithms, classical simulation methods, mixed-state phases of matter, and emerging approaches to quantum error mitigation and quantum error correction.
  arXiv  Detail & Related papers  (2025-12-21T15:55:12Z)
• Artificial intelligence for representing and characterizing quantum systems [49.29080693498154]
  Efficient characterization of large-scale quantum systems is a central challenge in quantum science.<n>Recent advances in artificial intelligence (AI) have emerged as a powerful tool to address this challenge.<n>This review discusses how each of these AI paradigms contributes to two core tasks in quantum systems characterization.
  arXiv  Detail & Related papers  (2025-09-05T08:41:24Z)
• Quantum-Accelerated Wireless Communications: Concepts, Connections, and Implications [59.0413662882849]
  Quantum computing is poised to redefine the algorithmic foundations of communication systems.<n>This article outlines the fundamentals of quantum computing in a style familiar to the communications society.<n>We highlight a mathematical harmony between quantum and wireless systems, which makes the topic more enticing to wireless researchers.
  arXiv  Detail & Related papers  (2025-06-25T22:25:47Z)
• Simulation of open quantum systems on universal quantum computers [15.876768787615179]
  We present an innovative and scalable method to simulate open quantum systems using quantum computers.<n>We define an adjoint density matrix as a counterpart of the true density matrix, which reduces to a mixed-unitary quantum channel.<n>Some long-time properties like steady states and the thermal equilibrium can also be investigated as the adjoint density matrix.
  arXiv  Detail & Related papers  (2024-05-31T09:07:27Z)
• 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)
• 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)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• Entanglement dynamics in hybrid quantum circuits [0.0]
  We review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits. We explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system.
  arXiv  Detail & Related papers  (2021-11-15T19:00:01Z)
• A thorough introduction to non-relativistic matrix mechanics in multi-qudit systems with a study on quantum entanglement and quantum quantifiers [0.0]
  This article provides a deep and abiding understanding of non-relativistic matrix mechanics. We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators. We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
  arXiv  Detail & Related papers  (2021-09-14T05:06:47Z)
• 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 information spreading in a disordered quantum walk [50.591267188664666]
  We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
  arXiv  Detail & Related papers  (2020-10-20T20:03:19Z)

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.