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arXiv · 2409.03656

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

Himanshu Sahu·Aranya Bhattacharya·Pingal Pratyush Nath
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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.

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Himanshu Sahu, Aranya Bhattacharya, Pingal Pratyush Nath. 2024-09-05. Quantum complexity and localization in random and time-periodic unitary circuits. https://doi.org/10.1103/mf2z-mrpd

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