Primal and dual hypergraphic representation for quantum circuits in hypergraphic partitioning

Quantum computing holds the promise of revolutionizing the way we solve complex problems by harnessing the principles of quantum mechanics. However, current noisy intermediate-scale quantum (NISQ) computers face significant limitations due to their small number of qubits and high error rates, making it challenging to execute large quantum circuits that require greater depth, size, or width. To address these challenges and enhance scalability, we conducted a comprehensive series of experiments involving hypergraph based methodologies for quantum circuit cutting, applicable to both spatial (distributing partitions across multiple processing units) and temporal (segmenting circuits for sequential execution) scenarios. Our experiments generated 13 distinct datasets, each capturing different aspects of quantum circuits and their hypergraph representations. These datasets include benchmark circuits with both independent and native gate sets, full circuits exhibiting maximal qubit connectivity, and randomly generated circuits, all represented in both primal hypergraphs (where qubits are vertices and gates are hyperedges) and dual hypergraphs (where qubits are hyperedges and gates are nodes). By providing OpenQASM files alongside their hypergraph representations, we ensured a comprehensive foundation for analyzing circuit cutting strategies. Leveraging hypergraph theory and advanced partitioning heuristics such as Stoer-Wagner, Fiduccia Mattheyses, and Kernighan-Lin, our approach aimed to optimize circuit cutting to reduce communication overhead in spatial distributions and minimize initialization costs in temporal sequences. The diverse datasets allowed us to evaluate the effectiveness of these heuristics across various circuit types and representations. To assess the quality of circuit partitions, we introduced a new metric called the coupling ratio, serving as a critical dimension in evaluating the balance between communication and initialization costs. Our comparative analysis demonstrated that hypergraph partitioning significantly improves the efficiency of distributed quantum computing architectures. Specifically, heuristics like Fiduccia Mattheyses proved to be flexible and fast, making them excellent choices for real-time circuit cutting processes in multi-QPU environments. The results of our research highlight the hypergraph partitioning process as a pivotal step in developing new reference architectures for quantum computers within distributed computing environments. By thoroughly describing the datasets from our experiments and analyzing their impact on circuit cutting strategies, we provide valuable insights that contribute to the practical advancement of scalable quantum computing.