Quantum computing promises to revolutionize various fields, yet the execution of quantum programs necessitates an effective compilation process. This involves strategically mapping quantum circuits onto the physical qubits of a quantum processor. The qubits' arrangement, or topology, is pivotal to the circuit's performance, a factor that often defies traditional heuristic or manual optimization methods due to its complexity. In this study, we introduce a novel approach leveraging reinforcement learning to dynamically tailor qubit topologies to the unique specifications of individual quantum circuits, guiding algorithm-driven quantum processor topology design for reducing the depth of mapped circuit, which is particularly critical for the output accuracy on noisy quantum processors. Our method marks a significant departure from previous methods that have been constrained to mapping circuits onto a fixed processor topology. Experiments demonstrate that we have achieved notable enhancements in circuit performance, with a minimum of 20\% reduction in circuit depth in 60\% of the cases examined, and a maximum enhancement of up to 46\%. Furthermore, the pronounced benefits of our approach in reducing circuit depth become increasingly evident as the scale of the quantum circuits increases, exhibiting the scalability of our method in terms of problem size. This work advances the co-design of quantum processor architecture and algorithm mapping, offering a promising avenue for future research and development in the field.

Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field.