Erlangen 2026 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 5: Quantum Mechanics: Spectral Theory and Many-Body Systems
MP 5.6: Talk
Wednesday, March 18, 2026, 15:15–15:30, KH 02.013
Complexity transitions in Krylov basis for random and time-periodic unitary circuits — Himanshu Sahu1,2,3, •Aranya Bhattacharya4,5, and Pingal Pratyush Nath6 — 1Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada. — 2Department of Physics and Astronomy and Institute for Quantum Computing,University of Waterloo, ON N2L 3G1, Canada. — 3Department of Physics and Department of Instrumentation & Applied Physics, Indian Institute of Sciences, C.V. Raman Avenue, Bangalore 560012, India. — 4Institute of Physics, Jagiellonian University, Lojasiewicza 11, 30-348 Krakow, Poland. — 5School of Mathematics, University of Bristol, Fry Building Woodland Road, Bristol BS8 1UG, UK — 6Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore 560012, India.
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 times proportional to d. 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, which we utilise to probe the transition between thermal and many-body localized phases.
Keywords: Random quantum circuits; Measurement-induced evolution; Complexity transition; Many-body localisation; Quantum chaos