Relational Quantum Circuit Synthesis via Topological Optimization

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.22272631

Related papers

Relational Quantum Circuit Synthesis via Tensor Network Optimization

Jincheng Zhang

The synthesis of efficient quantum circuits for complex computations remains a significant challenge in quantum computing. Traditional methods often struggle with the exponential growth of the solution space, particularly as the number of qubits increases. This work introduces a novel approach to quantum circuit synthesis leveraging tensor network optimization. We represent quantum circuits as tensor networks and employ techniques such as Tensor Train and Product Tensor Decomposition to efficiently approximate the optimal circuit topology. A quantum-inspired probabilistic sampling strategy is then integrated to explore the solution space effectively. The core claim is that optimizing quantum circuit synthesis for complex systems is intrinsically intractable using conventional methods. This approach offers a potentially scalable alternative, providing a pathway toward designing practical quantum circuits for a wider range of applications. The method is presented with a focus on the mathematical formalism and optimization techniques involved.

Aug 28, 20260 citations

Based Topological Optimization of Quantum Circuit Design Method

Jincheng Zhang

This paper presents a novel methodology for optimizing quantum circuit design utilizing topological optimization techniques. The core idea revolves around representing quantum circuits as topological networks and employing topological optimization algorithms to refine their structure. This approach aims to minimize the number of quantum gates required, thereby enhancing the efficiency and scalability of quantum computation. The research explores the potential of this method to significantly reduce circuit complexity and improve overall performance. The primary contribution lies in the application of topological optimization to the inherently complex domain of quantum circuit design, offering a potentially transformative approach to quantum computing. Mathematical formulations and key concepts are presented to illustrate the method's principles and demonstrate its feasibility.

Aug 28, 20260 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, 20260 citations

基于拓扑的量子计算的自适应量子电路设计

Jincheng Zhang

Quantum computing offers the potential for exponentially faster computations compared to classical computers, particularly for complex problems. However, the design and implementation of quantum circuits remain a significant challenge due to the inherent complexity of quantum systems. This paper explores a novel approach to quantum circuit design leveraging topological principles to automate the process of circuit optimization and achieve higher computational efficiency. We propose a new framework for automatic circuit adjustment based on topological structure, enabling the system to adapt its design based on the characteristics of the task at hand. This system aims to overcome the limitations of traditional methods by offering a more flexible and robust approach to quantum circuit creation. The research demonstrates the effectiveness of this framework through a series of simulations and analysis, showcasing its ability to generate circuits with improved performance for specific quantum algorithms. The core mechanism is the application of topological topological symmetries to the circuit structure, allowing the system to dynamically adjust parameters to achieve optimal results. This work represents a significant advancement in quantum circuit design, potentially paving the way for more efficient and scalable quantum computations.

Sep 4, 20260 citations

Adaptive Topology for Quantum Circuit Design

Jincheng Zhang

Quantum circuit design presents significant challenges due to the inherent fragility of quantum states and the complexity of controlling their evolution. Traditional methods often rely on static, pre-defined topologies, limiting the potential for optimization and adaptation to specific quantum systems. This paper introduces a novel approach to quantum circuit design, leveraging adaptive topology – a concept where the circuit's topology dynamically adjusts based on the quantum system's characteristics – to enhance circuit performance and stability. We propose a method for automatically generating and optimizing topological circuits using a reinforcement learning framework. The core mechanism involves a self-adaptive topological graph construction, iteratively refining the circuit's structure to minimize errors and maximize fidelity. The study demonstrates the effectiveness of this approach through simulations and experimental validation on a simplified quantum system, showing significant improvements in performance compared to conventional methods. The paper concludes with a discussion of the potential applications and future research directions in this rapidly evolving field.

Sep 6, 20260 citations

Dynamic Circuit Synthesis for Quantum Computing based on Graph Representation

Jincheng Zhang

Quantum circuit synthesis is a critical step in quantum computing, aiming to translate a logical quantum circuit into an efficient physical implementation. Traditional methods often suffer from inefficiency and a lack of adaptability, particularly when dealing with varying input data. This paper introduces a novel approach to quantum circuit synthesis that leverages graph representation and dynamic adaptation. The core idea is to represent quantum circuits as graphs, allowing the system to analyze and modify the circuit structure in real-time based on the input data. This dynamic adaptation minimizes gate count and execution time, offering significant improvements over static synthesis techniques. The presented framework provides a foundation for more flexible and efficient quantum computation.

Sep 3, 20260 citations