Related papers: Pre-training Tensor-Train Networks Facilitates Mac…

In this paper, we study trade-offs between efficiency, cost and accuracy when pre-training Transformer encoders with different pre-training objectives. For this purpose, we analyze features of common objectives and combine them to create…

Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…

Despite the advantage quantum computers are expected to deliver when performing simulations compared to their classical counterparts, the current noisy intermediate-scale quantum (NISQ) devices remain limited in their capabilities. The…

While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

We compare the performance of randomized classical and quantum neural networks (NNs) as well as classical and quantum-classical hybrid convolutional neural networks (CNNs) for the task of supervised binary image classification. We keep the…

Machine Learning with deep neural networks has transformed computational approaches to scientific and engineering problems. Central to many of these advancements are precisely tuned neural architectures that are tailored to the domains in…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Verifying quantum advantage for practical problems, particularly the ground state energy estimation (GSEE) problem, is one of the central challenges in quantum computing theory. For that purpose, dequantization algorithms play a central…

We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate…

We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…

Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…

Hybrid quantum-classical neural networks represent a promising frontier in the search for improved machine learning models. This thesis explores the integration of quantum layers within classical convolutional neural network architectures,…

Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…

Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…

The exploration of hybrid quantum-classical algorithms and programming models on noisy near-term quantum hardware has begun. As hybrid programs scale towards classical intractability, validation and benchmarking are critical to…

We introduce CL-QAS, a continual quantum architecture search framework that mitigates the challenges of costly amplitude encoding and catastrophic forgetting in variational quantum circuits. The method uses Tensor-Train encoding to…

The tensor-train (TT) format is a data-sparse tensor representation commonly used in high dimensional data approximations. In order to represent data with interpretability in data science, researchers develop data-centric skeletonized low…

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…