No abstract

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.

A1 C1 Fig. 1: The interface of VACSEN makes users aware of the quantum noise via three linked views (A-C). Computer Evolution View (A) allows the assessment for all quantum computers based on a temporal analysis for multiple performance metrics. Circuit Filtering View (B) supports the filtering for the potential optimal compiled circuits. Circuit Comparison View (C) supports the in-depth comparison regarding the performance of qubits or quantum gates and corresponding usages. The control panel (D) allows users to interactively configure the settings of VACSEN. Fidelity Comparison View (E) shows the fidelity distribution of each compiled circuit. Probability Distribution View (F) visualizes the results of state distribution of a quantum circuit execution.

It is common to compare state changes of multiple data items and identify which data items have changed more in various applications (e.g., annual GDP growth of different countries and daily increase of new COVID-19 cases in different regions). Grouped bar charts and slope graphs can visualize both state changes and their initial and final states of multiple data items, and are thus widely used for state change comparison. But they leverage implicit bar differences or line slopes to indicate state changes, which has been proven less effective for visual comparison. Both visualizations also suffer from visual scalability issues when an increasing number of data items need to be compared. This paper fills the research gap by proposing a novel radial visualization called Intercept Graph to facilitate visual comparison of multiple state changes. It consists of inner and outer axes, and leverages the lengths of line segments intercepted by the inner axis to explicitly encode the state changes. Users can interactively adjust the inner axis to filter large changes of their interest and magnify the difference of relatively-similar state changes, enhancing its visual scalability and comparison accuracy. We extensively evaluate Intercept Graph in comparison with baseline methods through two usage scenarios, quantitative metric evaluations, and well-designed crowdsourcing user studies with 50 participants. Our results demonstrate the usefulness and effectiveness of the Intercept Graph.

Figure 1: Comparison of a Intercept Graph(a) and other existing visualization tools for state change comparison, i.e. slope graphs (b) and grouped bar charts (c), representing the Points per Games (PPG) changes of 321 players across two seasons from a basketball statistics. The changes of PPG in two seasons before and after are indicated by intercepted line segment, line slopes and clustered bars' differences of (a), (b) and (c), respectively. (a)(left) accentuates players with top 30 PPG changes of the rising (left semi-circle, red) and dropping (right semi-circle, green) trends.