Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Graph-Based Quantum Computing Topological Optimization

Jincheng Zhang

Published Sep 2, 2026• 0 citations
Publisher

Abstract

This paper investigates the application of graph-based topology optimization to enhance the efficiency of quantum computation. Traditional approaches often focus on qubit count, while topology optimization provides a framework for structuring quantum circuits to minimize errors and maximize performance. We explore the integration of graph-based topology optimization into the design of quantum algorithms, specifically targeting topological quantum computing. The core claim is that leveraging graph structures and topology optimization can significantly improve the scalability and efficiency of quantum computations, offering a novel approach to addressing key challenges in the field.

DOI
10.5281/zenodo.22246280

Related papers

基于图的量子计算的拓扑结构

Jincheng Zhang

This paper explores the application of graph-based quantum computing frameworks, focusing on the utilization of graph topology for describing quantum circuit operations and performance optimization. We propose a novel approach to quantum algorithm design, leveraging graph structures to enhance computational efficiency and explore potential advancements in quantum computation. The core mechanism involves constructing quantum circuits as graphs, then utilizing graph topology to guide the design process, thereby improving the overall performance. We investigate the implications of this methodology within the context of quantum algorithms and outline future research directions.

•Aug 29, 2026•0 citations

Optimization Algorithms Based on Graph Theory for Quantum Computing

Jincheng Zhang

Quantum computing offers the potential for revolutionary advancements across diverse fields, demanding efficient algorithms and hardware architectures. Traditional optimization methods often overlook the inherent structural properties of quantum circuits, hindering their potential for optimal performance. This paper proposes a novel optimization algorithm based on graph theory, designed to leverage the structural characteristics of quantum circuits to enhance efficiency. The core mechanism involves representing quantum circuits as graphs, utilizing graph properties to guide the optimization process. We explore the application of this approach to optimize quantum circuit parameters, focusing on minimizing circuit depth and improving fidelity. The paper details the algorithm's architecture, the mathematical underpinnings of its optimization strategy, and preliminary results demonstrating its effectiveness in optimizing quantum circuits. The research highlights the potential of graph-based optimization to accelerate the development of practical quantum algorithms.

•Aug 31, 2026•0 citations

Quantum Error Correction Codes: Topological Optimization

Jincheng Zhang

This paper investigates the application of topological optimization techniques to quantum error correction codes. The core claim is that optimizing the topological structure of quantum error correction codes can significantly reduce error correction resource consumption and enhance the resilience of quantum computations. This is achieved through the utilization of topological optimization algorithms to identify optimal sub-graph structures within the topological network of a quantum error correction code, minimizing resource usage while maintaining sufficient error correction capability. We present a novel approach to quantum error correction design, moving beyond traditional code selection and offering a framework for dynamic code adaptation. The theoretical framework incorporates concepts from graph theory, linear algebra, and quantum information theory. The primary objective is to demonstrate a method for systematically reducing the overhead associated with quantum error correction, a critical step towards building fault-tolerant quantum computers. Our approach focuses on minimizing the number of physical qubits required to encode a logical qubit, a key metric for evaluating the efficiency of any quantum error correction scheme. The results indicate a substantial potential for optimization, suggesting a path toward more practical and scalable quantum computation.

•Sep 5, 2026•0 citations

Geometric Topology and Quantum Computing: A Unified Optimization Framework

Jincheng Zhang

This paper explores the synergistic potential of geometric topology and quantum computing for advanced optimization. We propose a novel framework that leverages the unique properties of quantum computation to accelerate and enhance the optimization of complex geometric structures. The core mechanism centers on constructing a quantum-enhanced optimization algorithm, specifically designed to effectively navigate and manipulate intricate geometric configurations. The research addresses the limitations of traditional optimization techniques by integrating geometric topology – a framework for understanding shapes and their properties – with the computational power of quantum systems. This integration promises to yield significant improvements in efficiency and scalability, offering a fundamentally new approach to geometric optimization. The study investigates the fundamental principles and potential applications of this joint approach, emphasizing its capacity to tackle problems currently intractable for classical optimization methods.

•Sep 6, 2026•0 citations

Relational Quantum Circuit Synthesis via Topological Optimization

Jincheng Zhang

Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.

•Sep 3, 2026•0 citations

Quantum Computing via Topological Structure Optimization

Jincheng Zhang

Quantum computing holds immense potential to revolutionize various fields, including drug discovery, materials science, and cryptography. However, current quantum algorithms often rely on precise, computationally intensive quantum circuits. This paper explores a novel approach to quantum computation that leverages the unique properties of topological structures to optimize quantum parameter sets, thereby enhancing computational efficiency. We propose a new algorithm based on topological optimization, demonstrating significant improvements over existing methods in specific benchmark problems. This research focuses on the fundamental principles of topological optimization and its application to quantum information processing. The core mechanism involves constructing a topological map representing the parameter space, guiding the search for optimal configurations through a gradient-based optimization process. We provide a detailed description of the algorithm, including the topological map construction, gradient calculation, and optimization procedure. The results showcase the effectiveness of this approach in improving quantum circuit performance and addressing limitations of traditional quantum algorithms.

•Sep 6, 2026•0 citations
This paper investigates the application of graph-based topology optimization to enhance the efficiency of quantum computation. Traditional approaches often focus on qubit count, while topology optimization provides a framework for structuring quantum circuits to minimize errors and maximize performance. We explore the integration of graph-based topology optimization into the design of quantum algorithms, specifically targeting topological quantum computing. The core claim is that leveraging graph structures and topology optimization can significantly improve the scalability and efficiency of quantum computations, offering a novel approach to addressing key challenges in the field.
This paper explores the application of graph-based quantum computing frameworks, focusing on the utilization of graph topology for describing quantum circuit operations and performance optimization. We propose a novel approach to quantum algorithm design, leveraging graph structures to enhance computational efficiency and explore potential advancements in quantum computation. The core mechanism involves constructing quantum circuits as graphs, then utilizing graph topology to guide the design process, thereby improving the overall performance. We investigate the implications of this methodology within the context of quantum algorithms and outline future research directions.
Quantum computing offers the potential for revolutionary advancements across diverse fields, demanding efficient algorithms and hardware architectures. Traditional optimization methods often overlook the inherent structural properties of quantum circuits, hindering their potential for optimal performance. This paper proposes a novel optimization algorithm based on graph theory, designed to leverage the structural characteristics of quantum circuits to enhance efficiency. The core mechanism involves representing quantum circuits as graphs, utilizing graph properties to guide the optimization process. We explore the application of this approach to optimize quantum circuit parameters, focusing on minimizing circuit depth and improving fidelity. The paper details the algorithm's architecture, the mathematical underpinnings of its optimization strategy, and preliminary results demonstrating its effectiveness in optimizing quantum circuits. The research highlights the potential of graph-based optimization to accelerate the development of practical quantum algorithms.
This paper investigates the application of topological optimization techniques to quantum error correction codes. The core claim is that optimizing the topological structure of quantum error correction codes can significantly reduce error correction resource consumption and enhance the resilience of quantum computations. This is achieved through the utilization of topological optimization algorithms to identify optimal sub-graph structures within the topological network of a quantum error correction code, minimizing resource usage while maintaining sufficient error correction capability. We present a novel approach to quantum error correction design, moving beyond traditional code selection and offering a framework for dynamic code adaptation. The theoretical framework incorporates concepts from graph theory, linear algebra, and quantum information theory. The primary objective is to demonstrate a method for systematically reducing the overhead associated with quantum error correction, a critical step towards building fault-tolerant quantum computers. Our approach focuses on minimizing the number of physical qubits required to encode a logical qubit, a key metric for evaluating the efficiency of any quantum error correction scheme. The results indicate a substantial potential for optimization, suggesting a path toward more practical and scalable quantum computation.
This paper explores the synergistic potential of geometric topology and quantum computing for advanced optimization. We propose a novel framework that leverages the unique properties of quantum computation to accelerate and enhance the optimization of complex geometric structures. The core mechanism centers on constructing a quantum-enhanced optimization algorithm, specifically designed to effectively navigate and manipulate intricate geometric configurations. The research addresses the limitations of traditional optimization techniques by integrating geometric topology – a framework for understanding shapes and their properties – with the computational power of quantum systems. This integration promises to yield significant improvements in efficiency and scalability, offering a fundamentally new approach to geometric optimization. The study investigates the fundamental principles and potential applications of this joint approach, emphasizing its capacity to tackle problems currently intractable for classical optimization methods.
Quantum circuit synthesis, the process of mapping logical operations onto a quantum hardware architecture, presents a significant bottleneck in the development of practical quantum computers. Traditional methods often suffer from exponential computational complexity, rendering them unsuitable for circuits of even moderate size. This work introduces a novel approach to quantum circuit synthesis leveraging topological optimization, a technique rooted in condensed matter physics. We represent quantum circuits as topological phases on a graph, where gate operations are encoded as transitions between these phases. An iterative optimization process then refines the graph structure, minimizing circuit complexity (represented as energy) while maintaining the desired quantum operations. The core of our method lies in the application of gradient-based optimization algorithms to this topological graph, driving the system towards a low-energy state representing an optimal quantum circuit. Preliminary results demonstrate the potential of this approach to significantly reduce gate count and improve fidelity compared to conventional synthesis methods. The proposed framework offers a scalable solution to the challenges inherent in quantum circuit design, paving the way for more efficient and reliable quantum computation.
Quantum computing holds immense potential to revolutionize various fields, including drug discovery, materials science, and cryptography. However, current quantum algorithms often rely on precise, computationally intensive quantum circuits. This paper explores a novel approach to quantum computation that leverages the unique properties of topological structures to optimize quantum parameter sets, thereby enhancing computational efficiency. We propose a new algorithm based on topological optimization, demonstrating significant improvements over existing methods in specific benchmark problems. This research focuses on the fundamental principles of topological optimization and its application to quantum information processing. The core mechanism involves constructing a topological map representing the parameter space, guiding the search for optimal configurations through a gradient-based optimization process. We provide a detailed description of the algorithm, including the topological map construction, gradient calculation, and optimization procedure. The results showcase the effectiveness of this approach in improving quantum circuit performance and addressing limitations of traditional quantum algorithms.