Hypergraphic Partitioning for Spatial and Temporal Quantum Circuit Cutting

Quantum computing holds immense promises for solving complex problems by leveraging quantum mechanics in a computational paradigm. However, challenges around the computational limitations of current noisy intermediate-scale quantum computers make it difficult to widely apply quantum advantages. These machines, with a limited number of qubits and high error rates, struggle to execute large quantum circuits, with higher dimensions of depth, size or width. To address those challenges, distributing circuits among processing agents or cutting circuits in small segments to be run in sequence are considered viable approaches to enhance scalability and computational power. The main goal for this paper is to present a hypergraphic representation approach for quantum circuit cutting, applicable to spatial and temporal scenario, using hypergraphic theory and heuristics. For each approach, the target is to reduce communication costs in the spatial scenario, and the initialization cost in the temporal scenario. To accomplish this, we apply heuristics for hypergraphic partitioning, considering the high level representation of the quantum circuit with different combinations of quantum gates. We compared results against different heuristics, such as Stoer-Wagner, Fiduccia-Mattheyses, and Kernighan-Lin, creating graphics based in a new circuit dimension called, coupling ratio for the circuit. The observed results from this method indicate the hypergraphic partitioning process as a critical step as part of a new reference architecture for quantum computers, in distributed quantum computing environments.