量子演算法可以透過量子電路實現，並且其電路被設計用於在理想的量子設備上實現計算。然而，理想的量子設備與目前的量子設備設備相去甚遠。目前的量子設備對於其量子位元之間的連接有很大的限制。該限制為，一個量子位元只允許與其最鄰近的量子位元有交互作用。目前的量子設備在執行計算前，必須先將量子位元放置於預先決定好的網格上。網格上各格點之間的連結進一步確定了量子設備的結構。在本文中，我們基於二維六方結構而不是二維笛卡爾結構來放置量子位元。為了驗證其有效性，我們設計一套流程將量子電路映射到預先決定的網格上，該流程由全局重排策略和局部重排策略組成。憑藉六方結構的優勢，與笛卡爾結構相比，使量子電路最鄰合規的成本顯著降低。此外，我們還提供了一套全面的分析，以更好地了解流程中各策略的貢獻。根據實驗結果，當網格類型由笛卡爾結構改變為六方結構時，全局重排策略對於小型量子電路至關重要。相比之下，對於大型量子電路，則是局部重排策略比全局重排策略更重要。

Quantum algorithms can be described as quantum circuits and are supposed to be carried out on an ideal quantum device which is far from current ones. The current quantum devices have a significant limitation on the connectivity between quantum bits. In other words, a quantum bit is only allowed to interact with its nearest neighbors. In reality, quantum bits have to be placed on a grid, where the connectivity between quantum bits is predefined. The predefined connectivity of a grid further determines the possible range of architectures of a quantum device after the placement of quantum bits. In this paper, we propose to place quantum bits based on a 2-D hexagonal architecture rather than a 2-D Cartesian architecture. To validate the effectiveness, we leverage a workflow for mapping nearest neighbor compliant quantum circuits onto targeting grids, where the workflow consists of a global reordering strategy and a local reordering strategy. With the advantages of the hexagonal grid, the overhead of making quantum circuits nearest neighbor compliant is reduced significantly compared with the Cartesian grid. We also provide a comprehensive set of ablation analyses to gain a better understanding of the contributions of the components within our workflow. According to the experimental results, when changing the grid type from Cartesian to hexagonal, the global reordering strategy is crucial for small quantum circuits. In contrast, the local reordering strategy is more important than the global reordering strategy for large quantum circuits.

Abstract (Chinese) I
Abstract II
Acknowledgements III
Contents IV
List of Figures VI
List of Tables VIII
List of Algorithms IX
1 Introduction 1
2 Background 4
2.1 HexagonalGrid ................................. 4
2.2 Nearest Neighbor Compliant Quantum Circuits ... 7
2.3 NearestNeighborCost ........................... 9
3 Related Works 12
3.1 GlobalReorderingStrategies .................... 12
3.2 LocalReorderingStrategies ..................... 13
4 Realizing NN Compliant Quantum Circuits 15
4.1 TheGlobalReorderingStrategy ................... 15
4.2 TheLocalReorderingStrategy .................... 18
5 Experimental Results 22
5.1 BenchmarkSuite ................................ 22
5.2 ExperimentalSetups ............................ 23
5.3 ResultsoftheConvertedNNCompliantCircuits ...... 24
6 Ablation Studies 31
6.1 DegradingtheGlobalReorderingStrategy .......... 31
6.2 DegradingtheLocalReorderingStrategy ........... 34
7 Conclusion 36
Bibliography 37

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