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Quantum machine learning (QML) has attracted considerable research interest, yet whether it offers practical benefits over classical approaches remains an open question. The choice of data encoding significantly influences QML performance,…

Circuit knitting offers a promising path to the scalable execution of large quantum circuits by breaking them into smaller sub-circuits whose output is recombined through classical postprocessing. However, current techniques face excessive…

Classical autoencoders are neural networks that can learn efficient low dimensional representations of data in higher dimensional space. The task of an autoencoder is, given an input $x$, is to map $x$ to a lower dimensional point $y$ such…

Although quantum machine learning has shown great promise, the practical application of quantum computers remains constrained in the noisy intermediate-scale quantum era. To take advantage of quantum machine learning, we investigate the…

Classically simulating quantum circuits is crucial when developing or testing quantum algorithms. Due to the underlying exponential complexity, efficient data structures are key for performing such simulations. To this end, tensor networks…

Quantized tensor trains (QTTs) are a multiscale computational framework that can potentially reduce the computational cost of solving partial differential equations and initial value problems by making low-rank approximations. However, its…

Recently, deep neural networks have proven capable of predicting some output properties of relevant random quantum circuits, indicating a strategy to emulate quantum computers alternative to direct simulation methods such as, e.g.,…

Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantage on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation, as the major reason for the barren…

While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Data encoding plays a fundamental and distinctive role in Quantum Machine Learning (QML). While classical approaches process data directly as vectors, QML may require transforming classical data into quantum states through encoding…

Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…

Pre-trained encoders are widely employed in dense prediction tasks for their capability to effectively extract visual features from images. The decoder subsequently processes these features to generate pixel-level predictions. However, due…

Quantum machine learning for classical data is currently perceived to have a scalability problem due to (i) a bottleneck at the point of loading data into quantum states, (ii) the lack of clarity around good optimization strategies, and…

We address the problem of implementing bottleneck layers from classical pre-trained neural networks on a quantum computer, with the goal of exploring intrinsically quantum ansatz for representing large linear layers within hybrid…

One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…

Multimodal Machine Translation (MMT) aims to improve translation quality by leveraging auxiliary modalities such as images alongside textual input. While recent advances in large-scale pre-trained language and vision models have…

Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks…

Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and…