Related papers: Fractal Path Strategies for Efficient 2D DMRG Simu…
Translating a general quantum circuit on a specific hardware topology with a reduced set of available gates, also known as transpilation, comes with a substantial increase in the length of the equivalent circuit. Due to decoherence, the…
Simultaneous localization and mapping (SLAM) systems with novel view synthesis capabilities are widely used in computer vision, with applications in augmented reality, robotics, and autonomous driving. However, existing approaches are…
We study the properties of the ground states of the one- and two-dimensional Hubbard models at half filling and moderate doping using entanglement-based measures, which we calculate numerically using the momentum-space density matrix…
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
Effective path planning is a pivotal challenge across various domains, from robotics to logistics and beyond. This research is centred on the development and evaluation of the Dynamic Curvature-Constrained Path Planning Algorithm (DCCPPA)…
We analyse the eigenvalue and eigenvector structure of the flip-flop quantum walk on regular graphs, explicitly demonstrating how it is quadratically faster than the classical random walk. Then we use it in a controlled spatial search…
Deceptive path planning (DPP) is the problem of designing a path that hides its true goal from an outside observer. Existing methods for DPP rely on unrealistic assumptions, such as global state observability and perfect model knowledge,…
In this work we develop the path integral optimization in a class of inhomogeneous 2d CFTs constructed by putting an ordinary CFT on a space with a position dependent metric. After setting up and solving the general optimization problem, we…
Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full…
Simultaneous localization and mapping (SLAM) plays a vital role in mapping unknown spaces and aiding autonomous navigation. Virtually all state-of-the-art solutions today for 2D SLAM are designed for dense and accurate sensors such as laser…
Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the…
Simulating quantum circuits on classical computers is a notoriously hard, yet increasingly important task for the development and testing of quantum algorithms. In order to alleviate this inherent complexity, efficient data structures and…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
We investigate the computational power of the recently introduced class of isometric tensor network states (isoTNSs), which generalizes the isometric conditions of the canonical form of one-dimensional matrix-product states to tensor…
We provide evidence that randomized low-rank factorization is a powerful tool for the determination of the ground state properties of low-dimensional lattice Hamiltonians through tensor network techniques. In particular, we show that…
We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…
The fields of entanglement theory and tensor networks have recently emerged as central tools for characterising quantum phases of matter. In this article, we determine the entanglement structure of ground states of gapped symmetric quantum…
We introduce an approach to compute reduced density matrices for local quantum unitary circuits of finite depth and infinite width. Suppose the time-evolved state under the circuit is a matrix-product state with bond dimension $D$; then the…
We propose the Selective Densification method for fast motion planning through configuration space. We create a sequence of roadmaps by iteratively adding configurations. We organize these roadmaps into layers and add edges between…
Recently, neural tangent kernel (NTK) has been used to explain the dynamics of learning parameters of neural networks, at the large width limit. Quantitative analyses of NTK give rise to network widths that are often impractical and incur…