Parallel Quantum Circuit Extraction from MBQC-Patterns

In the model of measurement-based quantum computing (MBQC), computations are performed via sequential measurements on a highly entangled graph state. MBQC is a natural model for photonic quantum computing and has been shown to be useful for tasks like optimization and verification of general quantum computations. Therefore, it is often necessary to translate between MBQC and the predominantly used quantum circuit model in a fast and reliable way. While there are algorithms with linear complexity to extract quantum circuits from measurement patterns using additional ancilla qubits, efficient ancilla-free extraction has shown to be more costly. We develop strategies to parallelize an existing extraction algorithm based on ZX-calculus by exploiting the graph structure of measurement patterns and evaluate the performance on patterns obtained from a benchmark set of quantum circuits. Our results suggest that possible parallelization speedups are closely related to the graph structure of a pattern.