Koen Mesman, Yinglu Tang, Matthias Moller, Boyang Chen, Sebastian Feld

Current quantum computers do not yet have the required qubit resources to meet the demands of most practical quantum algorithms. To circumvent this constraint, the practice of dividing these algorithms into parts through quantum circuit cutting has been explored. Many of these works either show exponential scaling or are far from optimal solutions. In this paper, MosaiQC is presented as a novel framework to improve upon existing circuit cutting frameworks. A hybrid warmstart with refinement optimization is used to find cutting solutions, allowing the combination of both wire and gate cuts. Additionally, MosaiQC enables hardware partitions of mixed sizes. Furthermore, the refinement stage incorporates a fast approximate quadratic assignment solver to better place hardware partitions, demonstrating a mean local fidelity improvement of $19.56 \% \pm 6.17\%$ over the baseline algorithm. In runtime and sampling overhead costs, improvements of $2.88 \times$ and an average of $16.84\%$ cut reduction (resulting in an average $5.83 \cdot 10^{11} \times$ overhead reduction) are observed. MosaiQC demonstrates a superior trade-off for run speed and solution quality, while adding fundamental features excluded by most competitors. With this, MosaiQC demonstrates that scalable heuristic optimization can substantially reduce the computational overhead of circuit-cut placement for increasingly large quantum circuits.