Related papers: Light cone tensor network and time evolution
Finding efficient tensor contraction paths is essential for a wide range of problems, including model counting, quantum circuits, graph problems, and language models. There exist several approaches to find efficient paths, such as the…
Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…
We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the…
This study addresses the problem of convolutional kernel learning in univariate, multivariate, and multidimensional time series data, which is crucial for interpreting temporal patterns in time series and supporting downstream machine…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear inverse function of the dynamical system can be approximated…
In tensor-network analysis of quantum many-body systems, it is of crucial importance to employ a tensor network with a spatial structure suitable for representing the state of interest. In the previous work [Hikihara et al., Phys. Rev.…
It is well known that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an…
Traffic problems have seriously affected people's life quality and urban development, and forecasting the short-term traffic congestion is of great importance to both individuals and governments. However, understanding and modeling the…
We propose a data-driven online convex optimization algorithm for controlling dynamical systems. In particular, the control scheme makes use of an initially measured input-output trajectory and behavioral systems theory which enable it to…
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…
Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…