Krylov's State Complexity and Information Geometry in Qubit Dynamics

• URL: http://arxiv.org/abs/2601.18941v1
• Date: Mon, 26 Jan 2026 20:22:52 GMT
• Title: Krylov's State Complexity and Information Geometry in Qubit Dynamics
• Authors: Carlo Cafaro, Emma Clements, Vishnu Vardhan Anuboyina,
• Abstract summary: We compare Krylov's state complexity with an information-geometric measure of complexity for the quantum evolution of two-level systems.<n>We show that the two measures reflect fundamentally different aspects of quantum dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and nonstationary Hamiltonians, corresponding to geodesic and nongeodesic trajectories. We formulate Krylov complexity in geometric terms, both instantaneously and in a time-averaged sense, and contrast it with an IG complexity of quantum evolutions characterized in terms of efficiency and curvature. We show that the two measures reflect fundamentally different aspects of quantum dynamics: Krylov's state complexity quantifies the directional spread of the evolving state relative to the initial state, whereas the IG complexity captures the effective volume explored along the trajectory on the Bloch sphere. This geometric distinction explains their inequivalent behavior and highlights the complementary nature of state-based and information-geometric notions of complexity in quantum systems.

Related papers

• Semiclassical entanglement entropy for spin-field interaction [41.99844472131922]
  We study a general bipartite quantum system consisting of a spin interacting with a bosonic field.<n>Our goal is to develop a semiclassical framework to describe the entanglement dynamics between these two subsystems.
  arXiv  Detail & Related papers  (2026-01-22T14:07:56Z)
• Symmetry-Resolved Spread Complexity [0.0]
  We investigate the impact of conserved charges on the dynamics of spread complexity of quantum states.<n>We identify speed limits that constrain the growth of complexity in the presence of conserved charges.
  arXiv  Detail & Related papers  (2025-09-16T12:03:23Z)
• Direct probing of the simulation complexity of open quantum many-body dynamics [42.085941481155295]
  We study the role of dissipation in simulating open-system dynamics using both quantum and classical methods.<n>Our results show that dissipation affects correlation length and mixing time in distinct ways at intermediate and long timescales.
  arXiv  Detail & Related papers  (2025-08-27T15:14:36Z)
• Krylov Complexity [0.0]
  We introduce and review a new complexity measure, called Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics.<n>We give a unified perspective on these topics, emphasizing the robust and most general features of K-complexity.<n>We mention and discuss a number of open problems related to K-complexity, underlining its currently very active status as a field of research.
  arXiv  Detail & Related papers  (2025-07-08T18:00:00Z)
• Krylov complexity of purification [0.0]
  purification can map mixed states into pure states and a non-unitary evolution into a unitary one by enlarging the Hilbert space.<n>We establish a connection between the complexities of mixed quantum states and their purification, proposing new inequalities among these complexities.
  arXiv  Detail & Related papers  (2024-08-01T18:00:00Z)
• Solving reaction dynamics with quantum computing algorithms [42.408991654684876]
  We study quantum algorithms for response functions, relevant for describing different reactions governed by linear response.<n>We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations.
  arXiv  Detail & Related papers  (2024-03-30T00:21:46Z)
• Quantifying High-Order Interdependencies in Entangled Quantum States [43.70611649100949]
  We introduce the Q-information: an information-theoretic measure capable of distinguishing quantum states dominated by synergy or redundancy. We show that quantum systems need at least four variables to exhibit high-order properties. Overall, the Q-information sheds light on novel aspects of the internal organisation of quantum systems and their time evolution.
  arXiv  Detail & Related papers  (2023-10-05T17:00:13Z)
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
  Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
  arXiv  Detail & Related papers  (2023-10-04T09:51:00Z)
• Krylov Complexity of Fermionic and Bosonic Gaussian States [9.194828630186072]
  This paper focuses on emphKrylov complexity, a specialized form of quantum complexity. It offers an unambiguous and intrinsically meaningful assessment of the spread of a quantum state over all possible bases.
  arXiv  Detail & Related papers  (2023-09-19T07:32:04Z)
• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds [0.0]
  We propose an information geometric theoretical construct to describe and understand the complex behavior of evolutions of quantum systems in pure and mixed states. We analytically show that the evolution of mixed quantum states in the Bloch ball is more complex than the evolution of pure states on the Bloch sphere.
  arXiv  Detail & Related papers  (2022-09-21T21:11:31Z)
• Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms [55.41644538483948]
  In particular, some steps of the implementation, as state preparation and readout processes, can surpass the complexity aspects of the algorithm itself. We present the complexity involved in the full implementation of quantum algorithms for solving linear systems of equations and linear system of differential equations.
  arXiv  Detail & Related papers  (2021-06-23T16:33:33Z)

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.