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The main approach to hybrid quantum-classical neural networks (QNN) is employing quantum computing to build a neural network (NN) that has quantum features, which is then optimized classically. Here, we propose a different strategy: to use…

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…

Let $G$ be an $n$-vertex graph with $m$ edges. When asked a subset $S$ of vertices, a cut query on $G$ returns the number of edges of $G$ that have exactly one endpoint in $S$. We show that there is a bounded-error quantum algorithm that…

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on…

Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…

As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…

Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…

We extend the ability of unitary quantum circuits by interfacing it with classical autoregressive neural networks. The combined model parametrizes a variational density matrix as a classical mixture of quantum pure states, where the…

Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…

Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…

Quantum machine learning is a rapidly growing field at the intersection of quantum technology and artificial intelligence. This review provides a two-fold overview of several key approaches that can offer advancements in both the…

Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…

The paper aims to investigate relevant computational issues of deep neural network architectures with an eye to the interaction between the optimization algorithm and the classification performance. In particular, we aim to analyze the…

Deep quantum neural networks may provide a promising way to achieve quantum learning advantage with noisy intermediate scale quantum devices. Here, we use deep quantum feedforward neural networks capable of universal quantum computation to…

A new challenge for learning algorithms in cyber-physical network systems is the distributed solution of big-data classification problems, i.e., problems in which both the number of training samples and their dimension is high. Motivated by…

A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…

The growing demands of remote detection and increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles…

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…