相关论文: On the solvable-unsolvable transition due to noise…

Precise qubit control in the presence of spatio-temporally correlated noise is pivotal for transitioning to fault-tolerant quantum computing. Generically, such noise can also have non-Gaussian statistics, which hampers existing…

The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…

We develop a recently introduced representation of quantum dynamics based on sampling negative Markov chain processes. By introducing particles and antiparticles, this formalism maps generic quantum dynamics onto a Markov process defined…

The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…

A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…

Uncertainty quantification (UQ) in scientific machine learning (SciML) becomes increasingly critical as neural networks (NNs) are being widely adopted in addressing complex problems across various scientific disciplines. Representative…

Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many…

While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum…

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully…

Data-driven predictive control (DDPC) has been recently proposed as an effective alternative to traditional model-predictive control (MPC) for its unique features of being time-efficient and unbiased with respect to the oracle solution.…

Turbulence has associated chaotic features. In the past couple of decades there has been growing interest in the study of these features as an alternative means of understanding turbulent systems. Our own input to this effort has been in…

Errors are the primary bottleneck preventing practical quantum computing. This challenge is exacerbated in the distributed quantum computing regime, where quantum networks introduce additional communication-induced noise. While error…

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory…

Recurrent neural networks (RNNs) with random, but sufficiently strong and balanced coupling display a well known high-dimensional chaotic dynamics. Here, we investigate if externally applied inputs to these RNNs can stabilize globally…

Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to…

The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…

There has been tremendous progress in the physical realization of quantum computing hardware in recent times, bringing us closer than ever before to realizing the promise of quantum computing. However, noise continues to pose a crucial…