A Noise-Aware Qubit Mapping Algorithm Evaluated via Qubit Interaction-Graph Criteria.

The qubit-mapping problem aims to assign qubits from a quantum circuit to a realistic NISQ device in order to maximize limited resources. Many algorithmic solutions for the qubit-mapping problem have been introduced, but much work remains in order to evaluate the effectiveness of a qubit-mapping algorithm with respect to mapping a circuit to devices while taking into account the noise characteristics of the device. In this work, we make progress on this question. Firstly, we introduce a noise-aware heuristic mapping algorithm which fares well when compared to brute-force and trivial mapping solutions for several benchmarks. This comparison serves to provide effective upper and lower bounds for our heuristic mapper in terms of an algorithm's success rate. Subsequently, we analyze how the performance of the mapping algorithm is affected by the characteristics of the interaction graph, which represents the interactions of qubits in a quantum circuit. We observe that as interaction-graph edges are added to benchmarks in either depth-first or breadth-first fashion, our heuristic algorithm's calculated success rate varies significantly, implying that both the amount of interaction-graph vertex degree and the distribution of edges in a quantum circuit's interaction graph play a significant role in the calculated success rate when our greedy heuristic maps to a quantum device's coupling graph. Lastly, we discovered that our heuristic algorithm provides substantial benefits over the trivial solution when mapping quantum circuits to QPUs, provided that less than approximately 75\% of the QPU is occupied. Lastly, as the size of the quantum processor in our simulation grows, so do the purported benefits from utilizing our heuristic mapper. This work takes the first steps towards the characterization of quantum algorithms with respect to efficient qubit-mapping solutions in NISQ-era devices.