與經典演算法相比，量子演算法具有巨大的速度優勢。然而，當前量子計算機中的實體量子位元並不能全部相互作用，對於不同的量子計算機具有不同的硬體限制。因此，在實際的量子計算機上執行量子演算法時，佈局合成是至關重要的一步，它確保量子演算法的合成電路能夠在符合硬體約束的情況下在量子計算機上順利運行。在本論文中，我們關注量子電路的佈局合成問題，並改進了先前的研究 (TB-OLSQ)，該研究使用過度區概念配合可滿足性模理論公式來解決。我們提出了如何修改先前研究的可滿足性模理論公式以獲得加速版本來減少執行時間。此外，我們還考慮閘吸收來擴展加速版本，以獲得更好的解決方案質量。我們的實驗結果表明，與先前研究相比，加速版本在一組不需要交換閘的電路中實現了121倍的加速，在另一組電路中，以不增加交換閘的情況下實現了6倍的加速，而在有閘吸收的版本中對於一組不需要交換閘的電路則快了115倍，而在另一組電路快3倍。對於需要交換閘的電路，閘吸收的功能有助於將電路的交換閘的數量減少38.9\%。

Compared to classical algorithms, quantum algorithms have a tremendous speed advantage. However, the physical qubits in current quantum computers do not all interact with each other, and different quantum computers have various hardware constraints. Therefore, in executing a quantum algorithm on an actual quantum computer, layout synthesis is a crucial step that ensures the synthesized circuit of the quantum algorithm can run smoothly on the quantum computer by complying with hardware constraints. In this thesis, we focus on a layout synthesis problem for quantum circuits and improve a prior work, TB-OLSQ, which adopts a transition-based SMT (Satisfiability Modulo Theories) formulation. We present how to modify TB-OLSQ to obtain an accelerated version for runtime reduction. In addition, we extend the accelerated version by considering gate absorption for better solution quality. Our experimental results show that compared with TB-OLSQ, the accelerated version achieves 121X speedup for a set of SWAP-free circuits and 6X speedup for the other set of circuits with no increase in SWAP gates, while the one with gate absorption is 115X faster for a set of SWAP-free circuits and is 3X faster for the other set of circuits. The one with gate absorption also helps reduce the number of SWAP gates by 38.9\% for the circuits requiring SWAP gates.

1 Introduction 1
2 Problem Formulations 8
2.1 Accelerated Version 8
2.2 Gate Absorption Version 9
3 Approaches 10
3.1 Preprocessing 10
3.1.1 Deletion of One-qubit Gates 10
3.1.2 Subgraph Identification 10
3.1.3 Construction of Spanning and Overlap Edge Sets 12
3.1.4 Construction of the Dependency List 12
3.2 Notations in each SMT Formulation 14
3.3 Transition-based SMT Formulation for Accelerated Version 15
3.3.1 Constant 15
3.3.2 Variables 15
3.3.3 Constraints 16
3.3.4 Differences from TB-OLSQ 18
3.3.5 Objective Function 19
3.4 Transition-based SMT Formulation for Gate Absorption Version 19
3.4.1 Variables 20
3.4.2 Constraints 20
3.5 Postprocessing 22
4 Experimental Results 23
4.1 Comparison among TB-OLSQ-ACC, TB-OLSQ, and [1] 23
4.2 Comparison among TB-OLSQ-GA, TB-OLSQ, and OLSQ-GA 24
5 Conclusion 27
References 28

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