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Physical Review D

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Krylov complexity is not a measure of distance between states or operators

Sergio E. Aguilar-Gutierrez1,* and Andrew Rolph2,3,†

  • 1Institute for Theoretical Physics, KU Leuven, 3001 Leuven, Belgium
  • 2Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1090 GL Amsterdam, The Netherlands
  • 3Theoretische Natuurkunde, Vrije Universiteit Brussel (VUB) and The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels, Belgium

  • *sergio.ernesto.aguilar@gmail.com
  • †andrew.d.rolph@gmail.com

Krylov Complexity in Early Universe

Ke-Hong Zhai and Lei-Hua Liu

Progress of Theoretical and Experimental Physics 2026 023E04 (2026)

Quantum complexity in gravity, quantum field theory, and quantum information science

Stefano Baiguera, Vijay Balasubramanian, Pawel Caputa, Shira Chapman, Jonas Haferkamp, Michal P. Heller, and Nicole Yunger Halpern

Physics Reports 1159 1 (2026)

Krylov complexity of a massless scalar field in massive BTZ black hole with quantum fluctuation

Yu-Ting Zhou and Xiao-Mei Kuang

Physics Letters B 881 140927 (2026)

A quantum computational perspective on spread complexity

Cameron Beetar, Eric L. Graef, Jeff Murugan, Horatiu Nastase, and Hendrik J.R. Van Zyl

Physics Letters B 878 140570 (2026)

Krylov Complexity of Purification

Rathindra Nath Das and Takato Mori

Phys. Rev. Lett. 136 030201 (2026)

Explicit connections between Krylov and Nielsen complexity

Ben Craps, Gabriele Pascuzzi, Juan F. Pedraza, Le-Chen Qu, and Shan-Ming Ruan

Phys. Rev. D 114 046024 (2026)

Krylov complexity and fidelity susceptibility in two-band Hamiltonians

Rishav Chaudhuri, Ayush Raj, Soham Ray, and Sai Satyam Samal

Phys. Rev. B 114 125134 (2026)

Krylov complexity in the ergodically constrained nonintegrable transverse-field Ising model

Gaurav Rudra Malik, Jeet Sharma, Rohit Kumar Shukla, S. Aravinda, and Sunil Kumar Mishra

Phys. Rev. B 113 184207 (2026)

A phase space approach to the wavefunction spreading and operator growth in the Krylov basis

Kunal Pal, Kuntal Pal, and Keun-Young Kim

J. High Energ. Phys. 2026 187 (2026)

CFT complexity and penalty factors

Stefano Baiguera, Nicolas Chagnet, Shira Chapman, and Osher Shoval

J. High Energ. Phys. 2026 247 (2026)

(A)Symmetric complexity and the Quantum Mpemba Effect

Cameron Beetar, Jeff Murugan, and Hendrik J. R. Van Zyl

J. High Energ. Phys. 2026 53 (2026)

Krylov’s state complexity and information geometry in qubit dynamics

Carlo Cafaro, Emma Clements, and Vishnu Vardhan Anuboyina

Eur. Phys. J. Plus 141 639 (2026)

Quantum dynamics in Krylov space: Methods and applications

Pratik Nandy, Apollonas S. Matsoukas-Roubeas, Pablo Martínez-Azcona, Anatoly Dymarsky, and Adolfo del Campo

Physics Reports 1125-1128 1 (2025)

Engineering quantum reservoirs through Krylov complexity, expressivity, and observability

Saud Čindrak, Lina Jaurigue, and Kathy Lüdge

Phys. Rev. Research 7 043190 (2025)

From Krylov complexity to observability: Capturing phase space dimension with applications in quantum reservoir computing

Saud Čindrak, Kathy Lüdge, and Lina Jaurigue

Phys. Rev. Research 7 L042039 (2025)

Multiseed Krylov Complexity

Ben Craps, Oleg Evnin, and Gabriele Pascuzzi

Phys. Rev. Lett. 134 050402 (2025)

Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum

Sergio E. Aguilar-Gutierrez, Hugo A. Camargo, Viktor Jahnke, Keun-Young Kim, and Mitsuhiro Nishida

Phys. Rev. D 112 126014 (2025)

Properties of Krylov state complexity in qubit dynamics

Siddharth Seetharaman, Chetanya Singh, and Rejish Nath

Phys. Rev. D 111 076014 (2025)

Statistics and complexity of wavefunction spreading in quantum dynamical systems

Yichao Fu, Keun-Young Kim, Kunal Pal, and Kuntal Pal

J. High Energ. Phys. 2025 139 (2025)

Brickwall one-loop determinant: spectral statistics & Krylov complexity

Hyun-Sik Jeong, Arnab Kundu, and Juan F. Pedraza

J. High Energ. Phys. 2025 154 (2025)

Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

Sergio E. Aguilar-Gutierrez, Yichao Fu, Kuntal Pal, and Klaas Parmentier

J. High Energ. Phys. 2025 39 (2025)

Aspects of complexity in quantum evolutions on the Bloch sphere

Carlo Cafaro, Emma Clements, and Abeer Alanazi

Eur. Phys. J. Plus 140 349 (2025)

Spread complexity and quantum chaos for periodically driven spin chains

Amin A. Nizami and Ankit W. Shrestha

Phys. Rev. E 110 034201 (2024)

Black holes and Marchenko-Pastur distribution

Wolfgang Mück

Phys. Rev. D 109 126001 (2024)

Spread complexity and localization in PT -symmetric systems

Aranya Bhattacharya, Rathindra Nath Das, Bidyut Dey, and Johanna Erdmenger

Phys. Rev. B 110 064320 (2024)

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