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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_62081_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">$k=\omega (\log n)$</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> <mo>=</mo> <mi>ω</mi> <mrow> <mo>(</mo> <mrow> <mi>log</mi> <mi>n</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41467_2025_62081_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="74" /> </InlineMediaObject> <EquationSource Format="TEX">${{{\rm{polylog}}}}(n)$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">polylog</mi> <mrow> <mo>(</mo> <mrow> <mi>n</mi> </mrow> <mo>)</mo> </mrow> </math></EquationSource> </InlineEquation> 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.

Pseudochaotic many-body dynamics as a pseudorandom state generator

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2025年7月23日

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Wonjun Lee,
Hyukjoon Kwon,
Gil Young Cho

摘要

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.