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Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
There have been significant advances in recent years in the development of forward error correction decoders that can decode codes of any structure, including practical realizations in synthesized circuits and taped out chips. While…
Continuous spectrum operators (CSOs), characterized by spectra comprising continuous intervals rather than discrete eigenvalues, are pivotal in quantum mechanics, wave propagation, and systems governed by partial differential equations.…
A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is…
Second-order methods for neural network optimization have several advantages over methods based on first-order gradient descent, including better scaling to large mini-batch sizes and fewer updates needed for convergence. But they are…
We propose a recipe on how to build a general, powerful, scalable (GPS) graph Transformer with linear complexity and state-of-the-art results on a diverse set of benchmarks. Graph Transformers (GTs) have gained popularity in the field of…
A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only…
Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process. This difficulty can be partly explained by the spectral…
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
This paper addresses explainability of the operator-regularization approach under the use of monotone Lipschitz-gradient (MoL-Grad) denoiser -- an operator that can be expressed as the Lipschitz continuous gradient of a differentiable…
We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those…
We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable…
The practical implementation difficulties arising from the Gaussian modulation of the GG02 protocol lead us to investigate the possibilities offered by the combination of probabilistic amplitude shaping technique and quadrature amplitude…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…
Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…
Fault-tolerant quantum computing demands decoders that are fast, accurate, and adaptable to circuit structure and realistic noise. While machine learning (ML) decoders have demonstrated impressive performance for quantum memory, their use…
Given a probability distribution $\mathcal{D}$ over the non-negative integers, a $\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\mathcal{D}$. For example, the binary deletion channel…
Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple…
Guessing random additive noise decoding (GRAND) is a noise-centric decoding method, which is suitable for ultra-reliable low-latency communications, as it supports high-rate error correction codes that generate short-length codewords. GRAND…