Generating pseudo-random unitaries with a Floquet driven chaotic quantum system

TL;DR

This paper demonstrates that a chaotic Floquet quantum system can generate pseudo-random unitaries, achieving approximate 3-designs with a small number of control parameters, useful for quantum information processing.

Contribution

It introduces a method to produce pseudo-random unitaries using ergodic Floquet systems with strong perturbations, expanding the toolkit for quantum randomness generation.

Findings

Uniform control parameters produce approximate 3-designs.

Parameter drift reduces the number of controls needed for 3-designs.

The system's ergodic behavior ensures broad phase space coverage.

Abstract

We explore using an ergodic Floquet quantum system on a torus to generate pseudo-random 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 4 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.