arXiv subjects

Haoqian Pan

Publications and source records attributed to Haoqian Pan.

6 recordsLinked to original sources

arXiv2026

Some experimental results on stable equivalence of GST Links for the Generalized Property R Conjecture

Gompf-Scharlemann-Thompson and Meier-Zupan constructed an infinite family of R-links that are potential counterexamples of the generalized property R conjecture. Their works also show that whether these links are stably handleslide trivial is an interesting open problem related to the Slice-Ribbon conjecture. In this work, we implement an algorithm to construct all these links explicitly, the details of this algorithm will the content of another paper. With such an algorithm, the stable handleslide triviality of some of these links is verified. Moreover, many links are shown to be stably handleslide equivalent. Some of the results are obtained independently in \cite{Knots in the fiber}

math.GT↗

arXiv2025

Application of the Quantum Approximate Optimization Algorithm in Solving the Total Domination Problem

Recent advancements in quantum computing have spurred substantial research into the application of quantum algorithms to combinatorial optimization problems. Among these challenges, the Total Domination Problem (TDP) emerges as a classic and critical paradigm in the field. For a graph G(V, E), TDP entails finding a minimal subset D subset of V that contains no isolated vertices, where every vertex not in D has at least one neighbor in D. TDP finds extensive applications across domains such as computer networks, social networks, and communications. Since the latter half of the last century, research efforts have focused on establishing its NP-completeness and developing solution algorithms, which have become foundational to combinatorial mathematics. Despite this rich history, the application of quantum algorithms to TDP remains largely underexplored. In this study, we present a pioneering application of the Quantum Approximate Optimization Algorithm (QAOA) to tackle TDP, evaluating its efficacy across a diverse set of parameters. This paper proves that the upper bound on the number of qubits required to solve TDP is 2|V| + |V| log_2( (2|E|)/|V| - 1 ). Our experimental findings demonstrate that QAOA is effective in addressing TDP: under most parameter combinations, it successfully computes a valid total dominating set (TDS). However, the algorithm's performance in identifying the optimal TDS is contingent upon specific parameter choices, revealing a significant bias in the distribution of effective parameter points. This research contributes valuable insights into the potential of quantum algorithms for solving TDP and lays a solid groundwork for future investigations in this area.

quant-ph↗

arXiv2025

Exploring the Potential of Quantum Approximate Optimization Algorithm in Tackling the Perfect Domination Problem

Perfect Domination Problem (PDP), a canonical challenge in combinatorial optimization, finds critical applications in real-world systems such as error-correcting codes, wireless communication networks, and social networks. Decades of research have firmly established its NP-completeness across numerous graph classes. Motivated by rapid advances in quantum computing, significant effort has recently been directed toward quantum algorithms for NP-complete problems, most notably the Quantum Approximate Optimization Algorithm (QAOA). Nonetheless, the applicability and efficacy of quantum approaches to the PDP remain entirely unexplored. This paper initiates the first systematic investigation of the PDP via QAOA. We evaluate solution quality on three benchmark instances of 6, 7, and 8 vertices using 15-18 qubits on a quantum simulator, examining more than 400 distinct parameter configurations. Experimental results confirm the algorithm's effectiveness and expose discernible trends in parameter selection. These outcomes substantiate QAOA's viability for the PDP and mark a seminal step toward situating this classical problem within the quantum-computing paradigm.

quant-ph↗

arXiv2024

Solving the Independent Domination Problem by Quantum Approximate Optimization Algorithm

In the wake of quantum computing advancements and quantum algorithmic progress, quantum algorithms are increasingly being employed to address a myriad of combinatorial optimization problems. Among these, the Independent Domination Problem (IDP), a derivative of the Domination Problem, has practical implications in various real-world scenarios. Despite this, existing classical algorithms for IDP are plagued by high computational complexity, and quantum algorithms have yet to tackle this challenge. This paper introduces a Quantum Approximate Optimization Algorithm (QAOA)-based approach to address the IDP. Utilizing IBM's qasm_simulator, we have demonstrated the efficacy of QAOA in solving IDP under specific parameter settings, with a computational complexity that surpasses that of classical methods. Our findings offer a novel avenue for the resolution of IDP.

quant-ph↗

arXiv2024

QUBO Formulations for Variation of Domination Problem

With the development of quantum computing, the use of quantum algorithms to solve combinatorial optimization problems on quantum computers has become a major research focus. The Quadratic Unconstrained Binary Optimization (QUBO) model serves as a bridge between combinatorial optimization problems and quantum computers, and is a prerequisite for these studies. In combinatorial optimization problems, the Domination Problem (DP) is related to many practical issues in the real world, such as the fire station problem, social network theory, and so on. Additionally, the DP has numerous variants, such as independent DP, total DP, k-domination, and so forth. However, there is a scarcity of quantum computing research on these variant problems. A possible reason for this is the lack of research on QUBO modeling for these issues. This paper investigates the QUBO modeling methods for the classic DP and its variants. Compared to previous studies, the QUBO modeling method we propose for the classic DP can utilize fewer qubits. This will lower the barrier for solving DP on quantum computers. At the same time, for many variants of DP problems, we provide their QUBO modeling methods for the first time. Our work will accelerate the entry of DP into the quantum era.

cs.CE↗

arXiv2023

Occupation Number Representation of Graph

In this paper, we propose a new way to represent graphs in quantum space. In that approach, we replace the rows of the adjacency matrix of the graph by state vectors in the occupation number representation. Unlike the traditional definition of graph states, we actually let the occupation number of a single-particle state denote the number of edges between each two adjacent vertices. This allows us to avoid taking into account the interaction between each two particles. Based on the creation and annihilation operators, we propose the edge creation and annihilation operators. With these two operators, we can implement the fundamental operation of adding and removing edges and vertices in a graph. Then all additional operations in the graph such as vertex contractions can be defined. Our method can be used to represent both simple and multigraphs. Directed and undirected graphs are also compatible with our approach. The method of representation proposed in this paper enriches the theory of graph representation in quantum space.

quant-ph↗