Related papers: Dyonic Objects and Tensor Network Representation
String theoretical ideas might be relevant for particle physics model building. Ideally one would hope to find a unified theory of all fundamental interactions. There are only few consistent string theories in D=10 or 11 space-time…
In this letter we investigate the possibility of observing macroscopic entanglement, considering realistic factors such as decoherence, particle losses, and measurements of limited precision (coarse-grained collective measurements). This…
Low-dimensional materials have attracted significant attentions over the past decade. To discover new low-dimensional materials, high-throughout screening methods have been applied in different materials databases. For this purpose, the…
Tensor network methods are powerful tools for studying quantum many-body systems. In this paper, we investigate the emergent statistical properties of random high-dimensional tensor-network states and the trainability of variational tensor…
Universal representation of geometric patterns of disordered matters is investigated with the aid of general topology. By utilizing the result obtained in the previous study (S. Ohmori, et.al., Phys. Scr. 94, 105213 (2019)) that any…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
The collective interference of partially distinguishable bosons in multi-mode networks is studied via double-sided Feynman diagrams. The probability for many-body scattering events becomes a multi-dimensional tensor-permanent, which…
We present tensor networks for feature extraction and refinement of classifier performance. These networks can be initialised deterministically and have the potential for implementation on near-term intermediate-scale quantum (NISQ)…
Convolutional Neural Network (CNN) features have been successfully employed in recent works as an image descriptor for various vision tasks. But the inability of the deep CNN features to exhibit invariance to geometric transformations and…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Tensor networks are a very powerful data structure tool originating from quantum system simulations. In recent years, they have seen increased use in machine learning, mostly in trainings with gradient-based techniques, due to their…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
Individuals interact with conspecifics in a number of behavioural contexts or dimensions. Here, we formalise this by considering a social network between n individuals interacting in b behavioural dimensions as a nxnxb multidimensional…
Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…
Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…
We introduce a deep neural network (DNN) framework called the \textbf{r}eal-space \textbf{a}tomic \textbf{d}ecomposition \textbf{net}work (\textsc{radnet}), which is capable of making accurate polarization and static dielectric function…
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete…