Related papers: Generating pseudo-random unitaries with a Floquet …
We develop a low-frequency perturbation theory in the extended Floquet Hilbert space of a periodically driven quantum systems, which puts the high- and low-frequency approximations to the Floquet theory on the same footing. It captures…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
We explore a very simple distribution of unitaries: random (binary) phase -- Hadamard -- random (binary) phase -- random computational-basis permutation. We show that this distribution is statistically indistinguishable from random Haar…
We investigate the spectral structure of reset-driven Floquet quantum channels generated by the Hamiltonian evolution of a many-body system followed by periodic resetting of a bath. By tuning a chaos-controlling parameter in the underlying…
We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet…
For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…
Recently the creation of novel topological states of matter by a periodic driving field has attracted great attention. To motivate further experimental and theoretical studies, we investigate interesting aspects of Floquet bands and…
We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged…
Our aim in this paper is twofold. Firstly, we develop a new asymptotic theory for Floquet exponents. We consider a linear system of differential equations with a time-periodic coefficient matrix. Assuming that the coefficient matrix depends…
Floquet engineering, the control of quantum systems using periodic driving, is an old concept in condensed matter physics, dating back to ideas such as the inverse Faraday effect. There is a renewed interest in this concept owing to the…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
We study the scattering of an electron from a one dimensional inverted Gaussian atomic potential in the presence of strong time periodic electric fields. Using Floquet theory, we construct the Floquet Scattering matrix in the…
We present a technique for derandomising large deviation bounds of functions on the unitary group. We replace the Haar distribution with a pseudo-random distribution, a k-design. k-designs have the first k moments equal to those of the Haar…
Strongly driven nonlinear systems are frequently encountered in physics, yet their accurate control is generally challenging due to the intricate dynamics. In this work, we present a non-perturbative, semi-analytical framework for tailoring…
The realization of unitary designs is of fundamental interest in quantum science and typically requires the ability to implement structured quantum circuits. Recent developments have explored the possibility of generating unitary designs…
We consider a finite-size periodically driven quantum system of coupled kicked rotors which exhibits two distinct regimes in parameter space: a dynamically-localized one with kinetic-energy saturation in time and a chaotic one with…
We derive a Cram\'er-Rao lower bound for the variance of Floquet multiplier estimates that have been constructed from stable limit cycles perturbed by noise. To do so, we consider perturbed periodic orbits in the plane. We use a periodic…