Related papers: On quantitative noise stability and influences for…
In this paper, we give a new proof of the classical KAM theorem on the persistence of an invariant quasi-periodic torus, whose frequency vector satisfies the Bruno-R\"ussmann condition, in real-analytic non-degenerate Hamiltonian systems…
In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f^2 = I. We describe several generalisations of well-known results in the theory of boolean functions, including…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
We present some results that complement our prequels [arXiv:1809.08425,arXiv:1907.05770] on holomorphic vector bundles. We apply the method of the Quot-scheme limit of Fubini-Study metrics developed therein to provide a generalisation to…
In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This…
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise. The spatial (resp. temporal) discretization is performed…
We study the robustness of quantum key distribution protocols using discrete or continuous variables to the channel noise. We introduce the model of such noise based on coupling of the signal to a thermal reservoir, typical for…
We prove stability estimates for the Bakry-Emery bound on Poincar\'e and logarithmic Sobolev constants of uniformly log-concave measures. In particular, we improve the quantitative bound in a result of De Philippis and Figalli asserting…
We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
We first prove the well-posedness of weak and strong solutions to the kinetic Cucker-Smale model in the Sobolev space with the initial data having compact velocity support. Then we study the kinetic Cucker-Smale model with noise. By…
The Demkov-Kunike (DK) model, characterized by a time-dependent Rabi coupling $J~\text{sech}(t/T)$ and on-site detuning $\Delta_0+\Delta_1\tanh(t/T)$, has one of the most general forms of an exactly solvable two-state quantum system, and,…
Periodically driven quantum many-body systems exhibit novel nonequilibrium states such as prethermalization, discrete time crystals, and many-body localization. Recently, the general mechanism of fractional resonances has been proposed that…
Recent work by Bravyi et al. constructs a relation problem that a noisy constant-depth quantum circuit (QNC$^0$) can solve with near certainty (probability $1 - o(1)$), but that any bounded fan-in constant-depth classical circuit (NC$^0$)…
Given a finite subset $F$ of integer points in $\mathbb Z^d$, it is of interest to seek conditions on $F$ that allow it to multi-tile $\mathbb Z^d$ by translations. To this end, we give a discretized version of the Bombieri-Siegel formula,…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
The reduced (in the angular coordinate $\phi$) wave equation and Klein-Gordon equation are considered on a Kerr background and in the framework of $C^{0}$-semigroup theory. Each equation is shown to have a well-posed initial value…
The classical Stein--Tomas theorem extends the theory of linear Fourier restriction estimates from smooth manifolds to fractal measures exhibiting Fourier decay. In the multilinear setting, transversality allows for Fourier extension…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
We provide Berry-Esseen bounds for sums of operator-valued Boolean and monotone independent variables, in terms of the first moments of the summands. Our bounds are on the level of Cauchy transforms as well as the L\'evy distance. As…