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Given a quantum circuit, a quantum computer can sample the output distribution exponentially faster in the number of bits than classical computers. A similar exponential separation has yet to be established in generative models through…

Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to…

Generating quantum data by learning the underlying quantum distribution poses challenges in both theoretical and practical scenarios, yet it is a critical task for understanding quantum systems. A fundamental question in quantum machine…

One of the most important properties of neural networks is the clustering of local minima of the loss function near the global minimum, enabling efficient training. Though generative models implemented on quantum computers are known to be…

Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…

With near-term quantum devices available and the race for fault-tolerant quantum computers in full swing, researchers became interested in the question of what happens if we replace a supervised machine learning model with a quantum…

This study explores the implementation of large Quantum Restricted Boltzmann Machines (QRBMs), a key advancement in Quantum Machine Learning (QML), as generative models on D-Wave's Pegasus quantum hardware to address dataset imbalance in…

Quantum computers offer the potential for efficiently sampling from complex probability distributions, attracting increasing interest in generative modeling within quantum machine learning. This surge in interest has driven the development…

One of the primary applications of classical Boltzmann machines is generative modeling, wherein the goal is to tune the parameters of a model distribution so that it closely approximates a target distribution. Training relies on estimating…

Quantum machine learning (QML) leverages quantum computing for classical inference, furnishes the processing of quantum data with machine-learning methods, and provides quantum algorithms adapted to noisy devices. Typically, QML proposals…

Quantum computers can efficiently sample from probability distributions that are believed to be classically intractable, providing a foundation for quantum generative modeling. However, practical training of such models remains challenging,…

As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…

We consider the computational model of IQP circuits (in which all computational steps are $X$ basis diagonal gates), supplemented by intermediate $X$ or $Z$ basis measurements. We show that if we allow non-adaptive or adaptive $X$ basis…

Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete…

Generative modeling is an unsupervised machine learning framework, that exhibits strong performance in various machine learning tasks. Recently we find several quantum version of generative model, some of which are even proven to have…

Quantum kernel methods (QKMs) offer an appealing framework for machine learning on near-term quantum computers. However, QKMs generically suffer from exponential concentration, requiring an exponential number of measurements to resolve the…

Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…

Are multi-layer parameterized quantum circuits (MPQCs) more expressive than classical neural networks (NNs)? How, why, and in what aspects? In this work, we survey and develop intuitive insights into the expressive power of MPQCs in…

Learning the true density in high-dimensional feature spaces is a well-known problem in machine learning. In this work, we consider generative autoencoders based on maximum-mean discrepancy (MMD) and provide theoretical insights. In…

Quantum computing holds significant potential to accelerate machine learning algorithms, especially in solving optimization problems like those encountered in Support Vector Machine (SVM) training. However, current QUBO-based Quantum SVM…