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

• URL: http://arxiv.org/abs/2409.03656v2
• Date: Tue, 20 May 2025 20:20:26 GMT
• Title: Quantum complexity and localization in random and time-periodic unitary circuits
• Authors: Himanshu Sahu, Aranya Bhattacharya, Pingal Pratyush Nath,
• Abstract summary: We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits.<n>Our numerical analysis encompasses two classes of random circuits: brick-wall random unitary circuits and Floquet random circuits.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the growth and saturation of Krylov spread (K-) complexity under random quantum circuits. In Haar-random unitary evolution, we show that, for large system sizes, K-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, K-complexity 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 K-complexity, forbye we utilize these saturation values to probe the transition between thermal and many-body localized phases.

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