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We consider the problem of computing shortest paths in a dense motion-planning roadmap $\mathcal{G}$. We assume that~$n$, the number of vertices of $\mathcal{G}$, is very large. Thus, using any path-planning algorithm that directly searches…
Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this…
In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that…
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing…
In order to optimize the ordering of the lattice sites in the momentum space and quantum chemistry versions of the density matrix renormalization group (DMRG) method we have studied the separability and entanglement of the target state for…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice…
Convolutional Neural Network (CNN)-based machine learning systems have made breakthroughs in feature extraction and image recognition tasks in two dimensions (2D). Although there is significant ongoing work to apply CNN technology to…
In this paper we explore a symmetry-based search space reduction technique which can speed up optimal pathfinding on undirected uniform-cost grid maps by up to 38 times. Our technique decomposes grid maps into a set of empty rectangles,…
We point out that area laws of quantum-information concepts indicate limitations of block transformations as well-behaved real-space renormalization group (RG) maps, which in turn guides the design of better RG schemes. Mutual-information…
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…
Currently, path planning algorithms are used in many daily tasks. They are relevant to find the best route in traffic and make autonomous robots able to navigate. The use of path planning presents some issues in large and dynamic…
Path planning is a classic problem for autonomous robots. To ensure safe and efficient point-to-point navigation an appropriate algorithm should be chosen keeping the robot's dimensions and its classification in mind. Autonomous robots use…
We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing the von Neumann entropy (known as entanglement entropy) and the entanglement contour in the scaling limit. Adopting quadratic fermionic models on…
We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size…
Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…
In this paper, we introduce FMapping, an efficient neural field mapping framework that facilitates the continuous estimation of a colorized point cloud map in real-time dense RGB SLAM. To achieve this challenging goal without depth, a…
Neural field-based SLAM methods typically employ a single, monolithic field as their scene representation. This prevents efficient incorporation of loop closure constraints and limits scalability. To address these shortcomings, we propose a…
Sampling-based algorithms are widely used for motion planning in high-dimensional configuration spaces. However, due to low sampling efficiency, their performance often diminishes in complex configuration spaces with narrow corridors.…
Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…