Improved Cost-Metric for Nearest Neighbor Mapping of Quantum Circuits to 2-Dimensional Hexagonal Architecture

Abstract

Quantum computing offers substantial speedup over conventional computing in solving certain computationally hard problems. The emergence of quantum computers in recent years has motivated researchers to develop design automation tools to map quantum circuits to such platforms. One major challenge is to limit the noise or computational error during gate operations; in particular, errors are higher when gates operate on non-neighbor qubits. A common approach to tackle this problem is to make the circuits Nearest-Neighbor (NN) compliant by inserting either Swap gates or CNOT templates. Reduction of gate overhead also becomes important as it serves to limit the overall noise and error. In some recent works, mapping of quantum circuits to hexagonal qubit architecture have been investigated. Hexagonal layout of qubits offers extended neighborhood that helps to reduce the number of Swap or additional CNOT gates required for NN-compliance. Existing approaches incur high gate overheads that can be reduced by improved gate mapping strategies with better cost metrics. The present work proposes one such approach using a priority-based cost metric. The proposed cost-metric is general and can be applied to any architectures; however, in this work we show its benefit for hexagonal architecture. Experiments on benchmark circuits confirm that the proposed method reduces gate overhead by $29\%$ over a very recent work based on greedy mapping.