Bipartite Graphs with DeepSeek

Imagine you have a group of people at a party, and you want to pair them up for a dance. A bipartite graph is like a dance chart where you have two separate groups of people, and each person from one group can only dance with someone from the other group. In simpler terms, it’s a way to connect two sets of things where connections only happen between the sets, not within the same set. For example, if you have a group of students and a group of books, a bipartite graph would show which student is reading which book, but it wouldn’t show connections between students or between books.

Bipartite graphs have many practical applications in real life. Here are a few examples:

1. Job Matching: Imagine you have a group of job seekers and a group of job openings. A bipartite graph can be used to match job seekers to job openings based on their skills and qualifications. Each job seeker is connected to the job openings they are qualified for, helping employers find the best candidates and job seekers find suitable positions.

2. Recommendation Systems: In online platforms like Netflix or Amazon, bipartite graphs can be used to recommend movies or products to users. One set of nodes represents users, and the other set represents items (movies, products, etc.). Connections between users and items indicate preferences or purchases, allowing the system to suggest items that similar users have liked.

3. Network Flow Problems: Bipartite graphs are used in network flow problems to optimize the flow of resources. For example, in transportation networks, they can help determine the most efficient way to route goods from suppliers to consumers, ensuring that supply meets demand.

4. Biological Networks: In biology, bipartite graphs can represent interactions between different types of entities, such as proteins and genes. This helps researchers understand how these entities interact and can lead to discoveries about biological processes and disease mechanisms.

5. Social Networks: Bipartite graphs can model relationships between two different types of entities in social networks, such as people and events. For example, they can show which people attended which events, helping to analyze social interactions and community structures.

DeepSeek was tasked with generating qiskit code to determine if a given graph is bipartite. The initial code did not function correctly. For example, one of the technical issues was that the circuit contained non-Clifford gates, such as multi-controlled phase operations, which were not supported by the stabilizer simulator. After several iterations and adjustments, the code was successfully modified to illustrate the bipartite concept.

Full report Respective notebook.