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Related papers: Krylov Complexity

200 papers

We examine the complexity of quasi-static chaotic open quantum systems. As a prototypical example, we analytically compute the Krylov complexity of a slowly leaking hard-sphere gas using Berry's conjecture. We then connect it to the…

High Energy Physics - Theory · Physics 2023-12-05 Vyshnav Mohan

The complexity of quantum evolutions can be understood by examining their dispersion in a chosen basis. Recent research has stressed the fact that the Krylov basis is particularly adept at minimizing this dispersion [V. Balasubramanian et…

Quantum Physics · Physics 2023-09-26 Gastón F. Scialchi , Augusto J. Roncaglia , Diego A. Wisniacki

Krylov complexity has recently emerged as a useful probe of operator growth and quantum dynamics in many-body systems and holographic dualities. In this paper we study its behavior in the Veneziano--Wosiek model, a supersymmetric matrix…

High Energy Physics - Theory · Physics 2026-03-24 Eleonora Alfinito , Matteo Beccaria

Krylov complexity is a measure of operator growth in quantum systems, based on the number of orthogonal basis vectors needed to approximate the time evolution of an operator. In this paper, we study the Krylov complexity of a…

High Energy Physics - Theory · Physics 2023-12-27 Cameron Beetar , Nitin Gupta , S. Shajidul Haque , Jeff Murugan , Hendrik J R Van Zyl

We perform a systematic holographic study of Krylov complexity for a wide class of confining quantum field theories. Using the geometric prescription that identifies the time derivative of the complexity with the proper momentum of a…

High Energy Physics - Theory · Physics 2026-05-28 Ali Fatemiabhari , Carlos Nunez

We extend the concept of Krylov complexity to include general unitary evolutions involving multiple generators. This generalization enables us to formulate a framework for generalized Krylov complexity, which serves as a measure of the…

High Energy Physics - Theory · Physics 2025-08-14 Amin Faraji Astaneh , Niloofar Vardian

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…

Quantum Physics · Physics 2026-01-28 Carlo Cafaro , Emma Clements , Vishnu Vardhan Anuboyina

The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is…

Quantum Physics · Physics 2024-04-15 Liangyu Chen , Baoyuan Mu , Huajia Wang , Pengfei Zhang

The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…

Quantum Physics · Physics 2024-08-14 Zongkang Zhang , Anbang Wang , Xiaosi Xu , Ying Li

We present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the…

High Energy Physics - Theory · Physics 2023-08-30 Mohsen Alishahiha , Souvik Banerjee

We investigate Krylov complexity in a simple quantum mechanical model describing a black hole coupled to its radiation. The model is constructed as a simplified ``mini-BMN" matrix system inspired by a recent proposal of Maldacena. Our aim…

High Energy Physics - Theory · Physics 2026-05-19 Eric L Graef , Jeff Murugan , Horatiu Nastase , Hendrik J. R. van Zyl

In this work, we investigate the Krylov complexity in quantum optical systems subject to time--dependent classical external fields. We focus on various interacting quantum optical models, including a collection of two--level atoms, photonic…

Quantum Physics · Physics 2024-09-09 Abhishek Chowdhury , Aryabrat Mahapatra

Krylov complexity has emerged as an important tool in the description of quantum information and, in particular, quantum chaos. Here we formulate Krylov complexity $K(t)$ for quantum mechanical systems as a path integral, and argue that at…

High Energy Physics - Theory · Physics 2026-02-20 Cameron Beetar , Eric L Graef , Jeff Murugan , Horatiu Nastase , Hendrik J R Van Zyl

Krylov complexity, a quantum complexity measure which uniquely characterizes the spread of a quantum state or an operator, has recently been studied in the context of quantum chaos. However, the definitiveness of this measure as a chaos…

Quantum Physics · Physics 2025-09-12 Sreeram PG , J. Bharathi Kannan , Ranjan Modak , S. Aravinda

Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state…

High Energy Physics - Theory · Physics 2024-05-27 Kyoung-Bum Huh , Hyun-Sik Jeong , Juan F. Pedraza

We study Krylov complexity in BMN Plane Wave Matrix Model at large mass deformation. We consider various consistent reductions of the matrix model that allow us to perform a Hamiltonian analysis which leads to different notions of the…

High Energy Physics - Theory · Physics 2026-05-26 Dibakar Roychowdhury

In this paper, we study the Krylov complexity ($K$) from the planar/inflationary patch of the de Sitter space using the two mode squeezed state formalism in the presence of an effective field having sound speed $c_s$. From our analysis, we…

High Energy Physics - Theory · Physics 2023-06-09 Kiran Adhikari , Sayantan Choudhury

One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at…

High Energy Physics - Theory · Physics 2025-10-10 Michal P. Heller , Jacopo Papalini , Tim Schuhmann

Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their…

High Energy Physics - Theory · Physics 2024-06-10 Pawel Caputa , Hyun-Sik Jeong , Sinong Liu , Juan F. Pedraza , Le-Chen Qu

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans…

High Energy Physics - Theory · Physics 2025-06-19 Kyoung-Bum Huh , Hyun-Sik Jeong , Leopoldo A. Pando Zayas , Juan F. Pedraza