Related papers: SchWARMA: A model-based approach for time-correlat…
We introduce the class of continuous-time autoregressive moving-average (CARMA) processes in Hilbert spaces. As driving noises of these processes we consider Levy processes in Hilbert space. We provide the basic definitions, show relevant…
Estimating the features of noise is the first step in a chain of protocols that will someday lead to fault tolerant quantum computers. The randomized benchmarking (RB) protocol is designed with this exact mindset, estimating the average…
In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…
The quantum Mpemba effect (QMPE), an intriguing anomalous relaxation phenomenon, has recently attracted significant attention. However, how various types of noise, which are ubiquitous in real systems, may affect the QMPE remains unknown.…
As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum…
We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In…
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical…
We propose a Weighted Autoregressive Varying gatE (WAVE) attention mechanism equipped with both Autoregressive (AR) and Moving-average (MA) components. It can adapt to various attention mechanisms, enhancing and decoupling their ability to…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the…
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The…
Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…
Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less…
Shallow quantum circuits are believed to be the most promising candidates for achieving early practical quantum advantage - this has motivated the development of a broad range of error mitigation techniques whose performance generally…
Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral…
Graph-based techniques emerged as a choice to deal with the dimensionality issues in modeling multivariate time series. However, there is yet no complete understanding of how the underlying structure could be exploited to ease this task.…
We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or…
The presence of correlations in noisy quantum circuits will be an inevitable side effect as quantum devices continue to grow in size and depth. Randomized Benchmarking (RB) is arguably the simplest method to initially assess the overall…
Complex time series models such as (the sum of) ARMA$(p,q)$ models with additional noise, random walks, rounding errors and/or drifts are increasingly used for data analysis in fields such as biology, ecology, engineering and economics…
The continuous development of new adaptive filters (AFs) based on novel cost functions (CFs) is driven by the demands of various application scenarios and noise environments. However, these algorithms typically demonstrate optimal…