Generating pseudo-random unitaries with a Floquet driven chaotic quantum system
Phys. Rev. A 113, 012436 – Published 23 January, 2026
DOI: https://doi.org/10.1103/bjpv-jwx6
Abstract
We explore using an ergodic Floquet quantum system on a torus to generate pseudorandom unitary operators. We choose a regime of the perturbed Harper model with strong perturbations and perturbation frequency exceeding the libration frequency to ensure that the system has an ergodic region that covers phase space and lacks resonant substructure. We generate a sample of unitary operators in a finite-dimensional space by computing Floquet propagators from a distribution of its control parameters. To compare the distribution of unitaries to that of a Haar-random distribution, we compute k-frame potentials from samples of numerically generated unitaries. We find that uniform distributions of four control parameters can generate an approximate 3-design. Distributions of fewer control parameters are required to create an approximate 3-design if the Floquet system parameters drift.
