Related papers: Quantization for spectral super-resolution
Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes…
This paper presents a comprehensive analysis of quantization techniques for optimizing Large Language Models (LLMs), specifically focusing on Post-Training Quantization (PTQ) and Quantization-Aware Training (QAT). Through empirical…
In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…
We introduce a correlated measurement noise model that can be efficiently described and characterized, and which admits effective noise-mitigation on the level of marginal probability distributions. Noise mitigation can be performed up to…
In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\alpha\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods,…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
We give tight statistical query (SQ) lower bounds for learnining halfspaces in the presence of Massart noise. In particular, suppose that all labels are corrupted with probability at most $\eta$. We show that for arbitrary $\eta \in…
Given a spectrally sparse signal $\mathbf{y} = \sum_{i=1}^s x_i\mathbf{f}(\tau_i) \in \mathbb{C}^{2n+1}$ consisting of $s$ complex sinusoids, we consider the super-resolution problem, which is about estimating frequency components…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
We investigate the compression of quantum information with respect to a given set $\mathcal{M}$ of high-dimensional measurements. This leads to a notion of simulability, where we demand that the statistics obtained from $\mathcal{M}$ and an…
Quantum symmetrization is the task of transforming a non-strictly increasing list of $n$ integers into an equal superposition of all permutations of the list (or more generally, performing this operation coherently on a superposition of…
Scalable quantum technologies will present challenges for characterizing and tuning quantum devices. This is a time-consuming activity, and as the size of quantum systems increases, this task will become intractable without the aid of…
The central issue in this article is to transmit a quantum state in such a way that after some decoherence occurs, most of the information can be restored by a suitable decoding operation. For this purpose, we incorporate redundancy by…
Quantum technologies rely heavily on accurate control and reliable readout of quantum systems. Current experiments are limited by numerous sources of noise that can only be partially captured by simple analytical models and additional…
Many datasets are obtained as a resolution trade-off between two adversarial dimensions; for example between the frequency and the temporal resolutions for the spectrogram of an audio signal, and between the number of wavelengths and the…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
This study presents a noise-robust framework for 1-bit diffraction tomography, a novel imaging approach that relies on intensity-only binary measurements obtained through coded apertures. The proposed reconstruction scheme leverages random…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Communication of quantized information is frequently followed by a computation. We consider situations of \emph{distributed functional scalar quantization}: distributed scalar quantization of (possibly correlated) sources followed by…
Quantization-aware training (QAT) is an effective method to drastically reduce the memory footprint of LLMs while keeping performance degradation at an acceptable level. However, the optimal choice of quantization format and bit-width…