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The Tucker decomposition expresses a given tensor as the product of a small core tensor and a set of factor matrices. Apart from providing data compression, the construction is useful in performing analysis such as principal component…
Quantization is commonly used in Deep Neural Networks (DNNs) to reduce the storage and computational complexity by decreasing the arithmetical precision of activations and weights, a.k.a. tensors. Efficient hardware architectures employ…
Commercial adiabatic quantum annealers have the potential to solve important NP-hard optimization problems efficiently. The newest generation of those machines additionally allows the user to customize the anneal schedule, that is, the…
This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds…
Current quantum annealing experiments often suffer from restrictions in connectivity in the sense that only certain qubits can be coupled to each other. The most common strategy to overcome connectivity restrictions so far is by combining…
Characterization of noise in current near-term quantum devices is of paramount importance to fully use their computational power. However, direct quantum process tomography becomes unfeasible for systems composed of tens of qubits. A…
We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. If a quantum code has a known tensor network construction of its encoding map, our method is far more efficient, and in…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Deep learning models are used in critical applications, in which mistakes can have serious consequences. Therefore, it is crucial to understand how and why models generate predictions. This understanding provides useful information to check…
Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. In this…
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
Collaborative filtering models generally perform better than content-based filtering models and do not require careful feature engineering. However, in the cold-start scenario collaborative information may be scarce or even unavailable,…
The entanglement distribution networks with various topologies are mainly implemented by active wavelength multiplexing routing strategies. However, designing an entanglement routing scheme, which achieves the maximized network connections…
Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems,…
Tensor network methods are powerful and efficient tools to study the properties and dynamics of statistical and quantum systems, in particular in one and two dimensions. In recent years, these methods were applied to lattice gauge theories,…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…