Related papers: Hyper-optimized tensor network contraction
Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
Quantum machine learning researchers often rely on incorporating Tensor Networks (TN) into Deep Neural Networks (DNN) and variational optimization. However, the standard optimization techniques used for training the contracted trainable…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
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…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
We discuss the variational optimization of a unitary tensor-network circuit with different network structures. The ansatz is performed based on a generalization of well-developed multi-scale entanglement renormalization algorithm and also…
Recently, deep neural networks have proven capable of predicting some output properties of relevant random quantum circuits, indicating a strategy to emulate quantum computers alternative to direct simulation methods such as, e.g.,…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…
Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a…
Tensor Networks are graph representations of summation expressions in which vertices represent tensors and edges represent tensor indices or vector spaces. In this work, we present EinExprs.jl, a Julia package for contraction path…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
Tensor methods have become a promising tool to solve high-dimensional problems in the big data era. By exploiting possible low-rank tensor factorization, many high-dimensional model-based or data-driven problems can be solved to facilitate…
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 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…
In the rapidly evolving field of quantum computing, tensor networks serve as an important tool due to their multifaceted utility. In this paper, we review the diverse applications of tensor networks and show that they are an important…
Recently, quantum computing has gained attention in urban studies as a tool for complex transport planning problems, but its role remains unclear. This paper reviews quantum computing research in urban transport planning and highlights…
Hybrid Tensor Networks (hTN) offer a promising solution for encoding variational quantum states beyond the capabilities of efficient classical methods or noisy quantum computers alone. However, their practical usefulness and many…
Recent advances in learning-based image compression typically come at the cost of high complexity. Designing computationally efficient architectures remains an open challenge. In this paper, we empirically investigate the impact of…
Random quantum circuit sampling serves as a benchmark to demonstrate quantum computational advantage. Recent progress in classical algorithms, especially those based on tensor network methods, has significantly reduced the classical…