Related papers: Local scale transformations on the lattice with te…
We investigate the potential of tensor network based machine learning methods to scale to large image and text data sets. For that, we study how the mutual information between a subregion and its complement scales with the subsystem size…
Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…
Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in…
Understanding entanglement remains one of the most intriguing problems in physics. While particle and site entanglement have been studied extensively, the investigation of length or energy scale entanglement, quantifying the information…
In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural…
An approximation algorithm is proposed to transform truncated QCD (or QED) series for observables. The approximation is a modification of the Baker-Gammel approximants, and is independent of the renormalization scale (RScl) $\mu$ -- the…
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local…
We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is…
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…
Photonic implementations of unitary processes on lattice structures, such as quantum walks, have been demonstrated across various architectures. However, few platforms offer the combined advantages of scalability, reconfigurability, and the…
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
Layer normalization (LN) is a fundamental component in modern deep learning, but its per-sample centering and scaling introduce non-negligible inference overhead. RMSNorm improves efficiency by removing the centering operation, yet this may…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models, in which the Hamiltonian is gradually simplified along a parallel…
We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer…
Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel…
As a first application of our renormalisation group approach to non-local matrix models [hep-th/0305066], we prove (super-)renormalisability of Euclidean two-dimensional noncommutative \phi^4-theory. It is widely believed that this model is…