Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator

TL;DR

This paper introduces pseudochaotic quantum many-body dynamics that, while distinct from true chaos, effectively generate pseudorandom states indistinguishable from Haar-random states, with efficient circuit implementations.

Contribution

It defines pseudochaotic dynamics, demonstrates their ability to produce pseudorandom states, and constructs efficient quantum circuits to realize these dynamics.

Findings

Pseudochaotic dynamics generate pseudorandom states.

A small subsystem can induce pseudochaotic behavior in larger systems.

Efficient quantum circuits produce pseudorandom states in polylogarithmic depth.

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 $k=\omega(\log n)$ 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 $\mathrm{polylog}(n)$ 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.