Pseudochaotic many-body dynamics as a pseudorandom state generator.

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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi> <mo>=</mo> <mi>ω</mi> <mrow><mo>(</mo> <mrow><mi>log</mi> <mi>n</mi></mrow> <mo>)</mo></mrow> </math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>polylog</mi> <mrow><mo>(</mo> <mrow><mi>n</mi></mrow> <mo>)</mo></mrow> </math> 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.