Pseudochaotic many-body dynamics as a pseudorandom state generator

Wonjun Lee (), Hyukjoon Kwon () and Gil Young Cho ()
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Wonjun Lee: Pohang University of Science and Technology
Hyukjoon Kwon: Korea Institute for Advanced Study
Gil Young Cho: Institute for Basic Science

Nature Communications, 2025, vol. 16, issue 1, 1-8

Abstract: Abstract Quantum chaos is central to understanding quantum dynamics and is crucial for generating random quantum states, a key resource for quantum information tasks. In this work, we introduce a new class of quantum many-body dynamics, termed pseudochaotic dynamics. Although distinct from chaotic dynamics, out-of-time-ordered correlators, the key indicators of quantum chaos, fail to distinguish them. Moreover, pseudochaotic dynamics generates pseudorandom states that are computationally indistinguishable from Haar-random states. We construct pseudochaotic dynamics by embedding a smaller k-qubit subsystem into a larger n-qubit system. We demonstrate that a subsystem of size $$k=\omega (\log n)$$ k = ω ( log n ) is sufficient to induce pseudochaotic behavior in the entire n-qubit system. Furthermore, we construct a quantum circuit exhibiting pseudochaotic dynamics and demonstrate that it generates pseudorandom states within $${{{\rm{polylog}}}}(n)$$ polylog ( n ) depth. In summary, our results constitute the discovery of new quantum dynamics that are computationally indistinguishable from genuine quantum chaos, which provides efficient routes to generate useful pseudorandom states.

Date: 2025
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DOI: 10.1038/s41467-025-62081-6

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