This thesis introduces and evaluates a novel rebalancing algorithm for optimizing tensor network contraction ordering. The algorithm is designed to minimize the parallelized contraction cost through local rebalancing operations performed on the contraction tree. Given the necessary hardware capabilities and software implementation, a reduced parallelized contraction cost leads to a shortened time to solution.
We conducted experiments on random quantum circuits generated using both Sycamore and Osprey qubit layouts, with 5, 10 and 15 qubits and with varying depth ranging from 3 to 12. We compared initial contraction trees generated by a standard greedy algorithm against those created using KaHyPar partitioning into four subtrees. Key findings include the fact that the rebalancing algorithm shows improved perfor-
mance as the circuit depth increases. It was also determined that KaHyPar partitioning significantly outperforms the greedy algorithm for initial contraction tree generation. Finally, we show that rebalancing at progressively deeper levels in the contraction tree yields further reductions to the parallelized contraction cost.