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IEEE Transactions on Visualization and Computer Graphics

QuRAFT: Enhancing Quantum Algorithm Design by Visual Linking Between Mathematical Concepts and Quantum Circuits

Zhen Wen, Jieyi Chen, Yao Lu, Siwei Tan, Jianwei Yin, Minfeng Zhu, Wei Chen

Published Dec 10, 2025• 0 citations
Publisher

Abstract

The emergence of quantum computers heralds a new frontier in computational power, empowering quantum algorithms to address challenges that defy classical computation. However, the design of quantum algorithms is challenging as it largely requires the manual efforts of quantum experts to transit mathematical expressions to quantum circuit diagrams. To ease this process, particularly for prototyping, educational, and modular design workflows, we propose to bridge the textual and visual contexts between mathematics and quantum circuits through visual linking and transitions. We contribute a design space for quantum algorithm design, focusing on the textual and visual elements, interactions, and design patterns throughout the quantum algorithm design process. Informed by the design space, we introduce QuRAFT, a visual interface that facilitates a seamless transition from abstract mathematical expressions to concrete quantum circuits. QuRAFT incorporates a suite of eight integrated visual and interaction designs tailored to support users in the formulation, implementation, and validation process of the quantum algorithm design. Through two detailed case studies and a user evaluation, this paper demonstrates the effectiveness of QuRAFT. Feedback from quantum computing experts highlights the practical utility of QuRAFT in algorithm design and provides valuable implications for future advancements in visualization and interaction design within the quantum computing domain.

DOI
10.1109/tvcg.2025.3642559

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The emergence of quantum computers heralds a new frontier in computational power, empowering quantum algorithms to address challenges that defy classical computation. However, the design of quantum algorithms is challenging as it largely requires the manual efforts of quantum experts to transit mathematical expressions to quantum circuit diagrams. To ease this process, particularly for prototyping, educational, and modular design workflows, we propose to bridge the textual and visual contexts between mathematics and quantum circuits through visual linking and transitions. We contribute a design space for quantum algorithm design, focusing on the textual and visual elements, interactions, and design patterns throughout the quantum algorithm design process. Informed by the design space, we introduce QuRAFT, a visual interface that facilitates a seamless transition from abstract mathematical expressions to concrete quantum circuits. QuRAFT incorporates a suite of eight integrated visual and interaction designs tailored to support users in the formulation, implementation, and validation process of the quantum algorithm design. Through two detailed case studies and a user evaluation, this paper demonstrates the effectiveness of QuRAFT. Feedback from quantum computing experts highlights the practical utility of QuRAFT in algorithm design and provides valuable implications for future advancements in visualization and interaction design within the quantum computing domain.
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Quantum computing is an emerging field that utilizes the unique principles of quantum mechanics to offer significant advantages in algorithm execution over classical approaches. This potential is particularly promising in the domain of quantum image processing, which aims to manipulate all pixels simultaneously. However, the process of designing and verifying these algorithms remains a complex and error-prone task. To address this challenge, new methods are needed to support effective debugging of quantum circuits. The Quantum Image Visualizer is an interactive visual analysis tool that allows for the examination of quantum images and their transformation throughout quantum circuits. The framework incorporates two overview visualizations that trace image evolution across a sequence of gates based on the most probable outcomes. Interactive exploration allows users to focus on relevant gates, and select pixels of interest. Upon selection, detailed visualizations enable in-depth inspection of individual pixels and their probability distributions, revealing how specific gates influence the likelihood of pixel color values and the magnitude of these changes. An evaluation of the Quantum Image Visualizer was conducted through in-depth interviews with eight domain experts. The findings demonstrate the effectiveness and practical value of our approach in supporting visual debugging of quantum image processing circuits.
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Quantum circuit synthesis is fundamental to the advancement and realization of quantum computing. To support both researchers and learners in exploring the structure and behavior of quantum circuits, this paper presents a dedicated interactive visualization platform specifically designed for quantum circuit synthesis: the Quantum Circuit Synthesis Visualizer (QSynViz). The platform offers intuitive circuit editing, matrix visualization, target-to-circuit distance computation, and dynamic tracking of the synthesis process. By making circuit structures and optimization trajectories visually accessible, QSynViz enables users to directly observe, analyze, and refine circuit designs. Bridging visual intuition with algorithmic insight, QSynViz serves as a powerful tool for circuit optimization, synthesis algorithm evaluation, and quantum computing education.
Quantum computing is a rapidly evolving field that enables exponential speed-up over classical algorithms. At the heart of this revolutionary technology are quantum circuits, which serve as vital tools for implementing, analyzing, and optimizing quantum algorithms. Recent advancements in quantum computing and the increasing capability of quantum devices have led to the development of more complex quantum circuits. However, traditional quantum circuit diagrams suffer from scalability and readability issues, which limit the efficiency of analysis and optimization processes. In this research, we propose a novel visualization approach for large-scale quantum circuits by adopting semantic analysis to facilitate the comprehension of quantum circuits. We first exploit meta-data and semantic information extracted from the underlying code of quantum circuits to create component segmentations and pattern abstractions, allowing for easier wrangling of massive circuit diagrams. We then develop Quantivine, an interactive system for exploring and understanding quantum circuits. A series of novel circuit visualizations is designed to uncover contextual details such as qubit provenance, parallelism, and entanglement. The effectiveness of Quantivine is demonstrated through two usage scenarios of quantum circuits with up to 100 qubits and a formal user evaluation with quantum experts. A free copy of this paper and all supplemental materials are available at https://osf.io/2m9yh/?view_only=0aa1618c97244f5093cd7ce15f1431f9.