# VENUS: A Geometrical Representation for Quantum State Visualization

arXiv: https://arxiv.org/abs/2303.08366 · HTML: https://mlsanity.com/paper/2303.08366/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2023.

## Built on by (most cited first, 4 of 4)

- [PristiQ: A Co-Design Framework for Preserving Data Security of Quantum Learning in the Cloud](https://mlsanity.com/paper/2404.13475/) (2024)
- [A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity](https://mlsanity.com/paper/2402.15333/) (2024)
- [Towards Explainable Quantum AI: Informing the Encoder Selection of Quantum Neural Networks via Visualization](https://mlsanity.com/paper/2512.14181/) (2025)
- [Quantum Cinema: An Interactive Cinematic Exploration of Quantum Computing Hardware via Generative World Models](https://mlsanity.com/paper/2606.17102/) (2026)

## Abstract (arXiv)

Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which leverages angles to represent quantum amplitudes. However, it cannot support the visualization of quantum entanglement and superposition, the two essential properties of quantum computing. To address this issue, we propose VENUS, a novel visualization for quantum state representation. By explicitly correlating 2D geometric shapes based on the math foundation of quantum computing characteristics, VENUS effectively represents quantum amplitudes of both the single qubit and two qubits for quantum entanglement. Also, we use multiple coordinated semicircles to naturally encode probability distribution, making the quantum superposition intuitive to analyze. We conducted two well-designed case studies and an in-depth expert interview to evaluate the usefulness and effectiveness of VENUS. The result shows that VENUS can effectively facilitate the exploration of quantum states for the single qubit and two qubits.