Work

Quantum complexity and localization in random and time-periodic unitary circuits

Year: 2026

Type: article

Abstract: We study the growth and saturation of complexity in Krylov basis in random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, this notion of complexity grows linearly before saturating at a late-time value of $d/2$, where $d$ is the Hilbert space dimension, at timescales $\sim d$. Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits. In brick-wall case, complexity in Krylov basis exhibits dynamics consistent with Haar-random unitary evolution, while the inclusion of measurements significantly slows its growth down. For Floquet random circuits, we show that localized phases lead to reduced late-time saturation values of the complexity enabling us to probe the transition between thermal and many-body localized phases.

Source: Physical review. B./Physical review. B

DOI: 10.1103/mf2z-mrpd

Authors: Himanshu Sahu, Aranya Bhattacharya, Pingal Pratyush Nath

Institutions: University of Waterloo, Perimeter Institute, Indian Institute of Science Bangalore, Jagiellonian University, University of Bristol

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green