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Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success…
Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a…
In this article we want to demonstrate the effectiveness of the new D-Wave quantum annealer, D-Wave 2000Q, in dealing with real world problems. In particular, it is shown how the quantum annealing process is able to find global optima even…
We investigate the use of quantum computing algorithms on real quantum hardware to tackle the computationally intensive task of feature selection for light-weight medical image datasets. Feature selection is often formulated as a k of n…
The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively…
Optimizing the training of a machine learning pipeline helps in reducing training costs and improving model performance. One such optimizing strategy is quantum annealing, which is an emerging computing paradigm that has shown potential in…
We present two new algorithms for approximating and updating the hierarchical Tucker decomposition of tensor streams. The first algorithm, Batch Hierarchical Tucker - leaf to root (BHT-l2r), proposes an alternative and more efficient way of…
The emerging edge computing has promoted immense interests in compacting a neural network without sacrificing much accuracy. In this regard, low-rank tensor decomposition constitutes a powerful tool to compress convolutional neural networks…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
Bayesian networks are widely used probabilistic graphical models, whose structure is hard to learn starting from the generated data. O'Gorman et al. have proposed an algorithm to encode this task, i.e., the Bayesian network structure…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular,…
Quantum computation offers exciting new possibilities for statistics. This paper explores the use of the D-Wave machine, a specialized type of quantum computer, which performs quantum annealing. A general description of quantum annealing…
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…