Exponential speedup of quantum algorithms for the pathfinding problem

Given $s, t$ in an unweighted undirected graph $G$, the goal of the pathfinding problem is to find an $s$-$t$ path. In this work, we first construct a graph $G$ based on welded trees and define a pathfinding problem in the adjacency list oracle $O$. Then we provide an efficient quantum algorithm to find an $s$-$t$ path in the graph $G$. Finally, we prove that no classical algorithm can find an $s$-$t$ path in subexponential time with high probability. The pathfinding problem is one of the fundamental graph-related problems. Our findings suggest that quantum algorithms may potentially offer advantages in more types of graphs to solve the pathfinding problem and open up new possibilities for practical applications of quantum computations in various fields.Comment: 10 pages,1 figur

Study on boundary search method for DFM mesh generation

The boundary mesh of the casting model was determined by direct calculation on the triangular facets extracted from the STL file of the 3D model. Then the inner and outer grids of the model were identified by the algorithm in which we named Inner Seed Grid Method. Finally, a program to automatically generate a 3D FDM mesh was compiled. In the paper, a method named Triangle Contraction Search Method (TCSM) was put forward to ensure not losing the boundary grids; while an algorithm to search inner seed grids to identify inner/outer grids of the casting model was also brought forward. Our algorithm was simple, clear and easy to construct program. Three examples for the casting mesh generation testified the validity of the program

Multidimensional Electrical Networks and their Application to Exponential Speedups for Graph Problems

Recently, Apers and Piddock [TQC '23] strengthened the natural connection between quantum walks and electrical networks by considering Kirchhoff's Law and Ohm's Law. In this work, we develop the multidimensional electrical network by defining Kirchhoff's Alternative Law and Ohm's Alternative Law based on the novel multidimensional quantum walk framework by Jeffery and Zur [STOC '23]. This multidimensional electrical network allows us to sample from the electrical flow obtained via a multidimensional quantum walk algorithm and achieve exponential quantum-classical separations for certain graph problems. We first use this framework to find a marked vertex in one-dimensional random hierarchical graphs as defined by Balasubramanian, Li, and Harrow [arXiv '23]. In this work, they generalised the well known exponential quantum-classical separation of the welded tree problem by Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman [STOC '03] to random hierarchical graphs. Our result partially recovers their results with an arguably simpler analysis. Furthermore, by constructing a $3$-regular graph based on welded trees, this framework also allows us to show an exponential speedup for the pathfinding problem. This solves one of the open problems by Li [arXiv '23], where they construct a non-regular graph and use the degree information to achieve a similar speedup. In analogy to the connection between the (edge-vertex) incidence matrix of a graph and Kirchhoff's Law and Ohm's Law in an electrical network, we also rebuild the connection between the alternative incidence matrix and Kirchhoff's Alternative Law and Ohm's Alternative Law. By establishing this connection, we expect that the multidimensional electrical network could have more applications beyond quantum walks.Comment: 39 page

DeepGATGO: A Hierarchical Pretraining-Based Graph-Attention Model for Automatic Protein Function Prediction

Automatic protein function prediction (AFP) is classified as a large-scale multi-label classification problem aimed at automating protein enrichment analysis to eliminate the current reliance on labor-intensive wet-lab methods. Currently, popular methods primarily combine protein-related information and Gene Ontology (GO) terms to generate final functional predictions. For example, protein sequences, structural information, and protein-protein interaction networks are integrated as prior knowledge to fuse with GO term embeddings and generate the ultimate prediction results. However, these methods are limited by the difficulty in obtaining structural information or network topology information, as well as the accuracy of such data. Therefore, more and more methods that only use protein sequences for protein function prediction have been proposed, which is a more reliable and computationally cheaper approach. However, the existing methods fail to fully extract feature information from protein sequences or label data because they do not adequately consider the intrinsic characteristics of the data itself. Therefore, we propose a sequence-based hierarchical prediction method, DeepGATGO, which processes protein sequences and GO term labels hierarchically, and utilizes graph attention networks (GATs) and contrastive learning for protein function prediction. Specifically, we compute embeddings of the sequence and label data using pre-trained models to reduce computational costs and improve the embedding accuracy. Then, we use GATs to dynamically extract the structural information of non-Euclidean data, and learn general features of the label dataset with contrastive learning by constructing positive and negative example samples. Experimental results demonstrate that our proposed model exhibits better scalability in GO term enrichment analysis on large-scale datasets.Comment: Accepted in BIOKDD'2

Families of weighted sum formulas for multiple zeta values

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.Comment: The conjecture at the end is reformulate