Quantum simulation is the foundation for the design of many algorithms which share subroutines known as quantum simulation kernels. Optimizing the compilation of these kernels is crucial, involving two key components: 1) circuit synthesis and 2) qubit mapping. However, existing circuit synthesis methods either overlook qubit connectivity constraints (QCCs) or prioritize minimizing gate count over optimizing circuit depth. Similarly, current qubit mapping techniques do not work well with circuit synthesis methods. To address these limitations, we propose PauliForest, which comprises a connectivity-aware circuit synthesis algorithm and a Pauli-oriented qubit mapping algorithm. The synthesis algorithm employs heuristic strategies to generate shallower circuits, while the qubit mapping algorithm seamlessly collaborates with the circuit synthesis process. Compared to the state-of-the-art Paulihedral compiler, our approach significantly reduces both CNOT gate counts (by 13%) and circuit depths (by 25%). Experiments on a noisy simulator and a real superconducting quantum computer show that our algorithm can improve the fidelity of quantum circuit execution compared to Paulihedral.

As a less developed but potential quantum technology, neutral atoms (NAs) can provide advantages, including higher qubit connectivity, longer-range interactions, and much more native multicontrol gates than superconductivity. Long-range interactions, however, prevent parallelism of interacting qubit pairs with their surrounding restriction zones. Therefore, the quantum program cannot be run directly on an NA quantum computer (NAQC) unless compiled. The recent compiling study of NAQC applies simple layer-by-layer scheduling and does not consider the difference in gate duration. To address the above issues, we focus on the qubit mapping and quantum gate scheduling (M&S) problem of quantum circuits to meet hardware constraints of superconductivity and even NAs. Our goal is to shorten the execution time to mitigate decoherence noise. We propose a block-game-like abstraction mechanism TETRIS which is an abstract model of the M&S problem and aware of the duration difference of gates and several other NA characteristics. Based on the abstraction, we propose a heuristic greedy algorithm (HGA) to solve the M&S problem efficiently. To further speed up the execution of the circuit, we embed HGA into a Monte Carlo tree search (MCTS) framework to solve the M&S problem, which consumes more compiling time but achieves a better result. Comparing our MCTS algorithm with the only recent M&S algorithm for NAQC, the average speedup ratio is$1.75\times $for several quantum circuits collected from RevLib, and$1.18\times $for circuits from Qiskit Lib.

Due to multiple limitations of quantum computers in the NISQ era, quantum compilation efforts are required to efficiently execute quantum algorithms on NISQ devices Program rewriting based on pattern matching can improve the generalization ability of compiler optimization. However, it has rarely been explored for quantum circuit optimization, further considering physical features of target devices.