Related papers: Fast Tensor Disentangling Algorithm
We develop fast spectral algorithms for tensor decomposition that match the robustness guarantees of the best known polynomial-time algorithms for this problem based on the sum-of-squares (SOS) semidefinite programming hierarchy. Our…
We search for efficient disentanglers on random Clifford circuits of two-qubit gates arranged in a brick-wall pattern, using the proximal policy optimization (PPO) algorithm \cite{schulman2017proximalpolicyoptimizationalgorithms}.…
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix…
Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…
Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for…
In this paper we propose new techniques to sample arbitrary third-order tensors, with an objective of speeding up tensor algorithms that have recently gained popularity in machine learning. Our main contribution is a new way to select, in a…
Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…
Optimized quantum control can enhance the performance and noise resilience of quantum metrology. However, the optimization quickly becomes intractable when multiple control operations are applied sequentially. In this work, we propose…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
In this work, we study the tensor ring decomposition and its associated numerical algorithms. We establish a sharp transition of algorithmic difficulty of the optimization problem as the bond dimension increases: On one hand, we show the…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Efficient and fast computation of a tensor singular value decomposition (t-SVD) with a few passes over the underlying data tensor is crucial because of its many potential applications. The current/existing subspace randomized algorithms…