Algorithm-Aware Qubit Mapping
Algorithm-aware (AlgAw) qubit mapping aims at directly providing the solutions to qubit mapping of algorithms with regular structures based on the algorithm's features. Although exact methods can provide high quality solutions, their compilation time grows exponentially with circuit size. To improve scalability, we propose the AlgAw qubit mapping approach. The main idea is to first identify subcircuits in an algorithm to be mapped, then analyze optimal solutions for small scale subcircuits found by exact methods, extend these solutions to large scale subcircuits, reconstruct the entire circuit and assign parameters, and finally map pretranspiled circuits onto the target quantum devices. Applying AlgAw to the quantum approximate optimization algorithm (QAOA) on linear and T-shaped subtopologies produces optimal and scalable solutions for arbitrary numbers of qubits and depths, which is critical to the algorithm's performance on near-term quantum devices. Compared to other methods including Qiskit, Tket, and SWAP-network, AlgAw produces the least number of CNOT gates and the lowest circuit depth for the pretranspiled circuits. Furthermore, AlgAw takes only a few seconds to construct a resulting circuit having a hundred qubits. The benchmarking results on IBM quantum devices show that AlgAw qubit mapping yields better performance than others. AlgAw is applicable to other variational quantum algorithms (VQAs) and can also be applied to other algorithms.
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