Hypergraphic representation for adaptive quantum circuits

Abstract: Adaptive quantum circuits enhance flexibility and efficiency over traditional static circuits by dynamically adjusting their structure and parameters in real-time based on intermediate measurement outcomes. This paper introduces a novel hypergraph representation for adaptive quantum circuits, where groups of gates are considered as participants of hyperedges. By incorporating these gate groups into hyperedges, we create an extended hypergraph that includes constraints usable during the partitioning process. This approach guides the partitioning to maintain groups of ports associated with classical operations, ensuring that the resulting partitions prioritize qubits involved in the same sections of classical operations inherent to the adaptive approach. We present a new hypergraph partitioning algorithm based as an extension of Fiduccia-Mattheyses heuristic, to support hypergraphs created from adaptive quantum circuits. Comparative analysis between static and adaptive methods demonstrates the effectiveness of the proposed hypergraph techniques for adaptive circuits. Experimental results using benchmark quantum circuits validate our theoretical insights, showing improvements in circuit representation for partitioning heuristics. These findings highlight the practical benefits of hypergraph representation in adaptive quantum computing.