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In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

数值分析 · 数学 2014-04-09 Alexander Litvinenko , Hermann G. Matthies

With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…

量子物理 · 物理学 2017-08-29 Pablo Arrighi , Gilles Dowek

Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…

量子物理 · 物理学 2019-02-12 Alessio Benavoli , Alessandro Facchini , Marco Zaffalon

The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…

量子物理 · 物理学 2009-10-31 Valerio Scarani

Target Propagation (TP) algorithms compute targets instead of gradients along neural networks and propagate them backward in a way that is similar yet different than gradient back-propagation (BP). The idea was first presented as a…

机器学习 · 计算机科学 2021-12-03 Vincent Roulet , Zaid Harchaoui

Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…

量子物理 · 物理学 2019-09-09 Jonathan Allcock , Chang-Yu Hsieh , Iordanis Kerenidis , Shengyu Zhang

The main deficiency of the algorithms running on digital computers nowadays is their inability to change themselves during the execution. In line with this, the paper introduces the so-called replicated algorithms, inspired by the concept…

神经与进化计算 · 计算机科学 2023-04-27 Iztok Fister , Iztok Fister

A causal set C can describe a discrete spacetime, but this discrete spacetime is not quantum, because C is endowed with Boolean logic, as it does not allow cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we consider a…

广义相对论与量子宇宙学 · 物理学 2007-05-23 P. A. Zizzi

Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they facilitate a complete characterization of uncertainty…

机器学习 · 统计学 2023-04-25 Steven Winter , Trevor Campbell , Lizhen Lin , Sanvesh Srivastava , David B. Dunson

We consider quantum and private communications assisted by repeaters, from the basic scenario of a single repeater chain to the general case of an arbitrarily-complex quantum network, where systems may be routed through single or multiple…

量子物理 · 物理学 2017-08-17 Stefano Pirandola

Large multilayer neural networks trained with backpropagation have recently achieved state-of-the-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a…

机器学习 · 统计学 2015-07-16 José Miguel Hernández-Lobato , Ryan P. Adams

This thesis treats networks providing quantum computation based on distributed paradigms. Compared to architectures relying on one processor, a network promises to be more scalable and less fault-prone. Developing a distributed system able…

量子物理 · 物理学 2023-07-18 Daniele Cuomo

In a reversible language, any forward computation can be undone by a finite sequence of backward steps. Reversible computing has been studied in the context of different programming languages and formalisms, where it has been used for…

编程语言 · 计算机科学 2016-08-22 Naoki Nishida , Adrián Palacios , Germán Vidal

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…

量子物理 · 物理学 2021-11-19 Dmitri Maslov , Jin-Sung Kim , Sergey Bravyi , Theodore J. Yoder , Sarah Sheldon

The notion of programming paradigms, with associated programming languages and methodologies, is a well established tenet of Computer Science pedagogy, enshrined in international curricula. However, this notion sits ill with Kuhn's classic…

编程语言 · 计算机科学 2020-02-17 Greg Michaelson

Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…

量子物理 · 物理学 2009-11-07 Jose P. Palao , Ronnie Kosloff

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is…

Artificial intelligence algorithms largely build on multi-layered neural networks. Coping with their increasing complexity and memory requirements calls for a paradigmatic change in the way these powerful algorithms are run. Quantum…

According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…

量子物理 · 物理学 2007-05-23 P. Gralewicz

Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been…

机器学习 · 计算机科学 2020-10-07 Beren Millidge , Alexander Tschantz , Christopher L. Buckley