Related papers: An exact tensor network for the 3SAT problem
The 3-Satisfiability Problem (3-SAT) is a demanding combinatorial problem, of central importance among the non-deterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence and logistics. Even…
Tensor networks, originally designed to address computational problems in quantum many-body physics, have recently been applied to machine learning tasks. However, compared to quantum physics, where the reasons for the success of tensor…
Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…
Exact many-body quantum problems are known to be computationally hard due to the exponential scaling of the numerical resources required. Since the advent of the Density Matrix Renormalization Group, it became clear that a successful…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is…
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors.…
Although tensor network states constitute a broad range of exotic quantum states, their realization is challenging and often requires resources whose depth scales with system size. In this work, we explore criteria on the local tensors for…
We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…
The Inverse 3-SAT problem is known to be coNP Complete. This article shows a new interesting way to solve directly the problem by using closure under resolution and partial assignment properties. An algorithm is proposed which lets solve…
Modern quantum optical systems such as photonic quantum computers and quantum imaging devices require great precision in their designs and implementations in the hope to realistically exploit entanglement and reach a real quantum advantage.…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
We determine the computational power of preparing Projected Entangled Pair States (PEPS), as well as the complexity of classically simulating them, and generally the complexity of contracting tensor networks. While creating PEPS allows to…
We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in…
Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a…
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…