基於蒙地卡羅樹搜尋增強式學習的邏輯考量量子繞線

Abstract

本研究提出了 LAUREL，一個專為解決量子繞線難題而設計的框架，目標是同時減少量子電路的電路深度和閘門數量。LAUREL 引入了量子運算依賴圖來建模增強式學習（RL）的狀態，使得在等價的量子電路中探索不同的量子邏輯閘執行順序成為可能。 該框架創建了一個基於依賴圖的前瞻窗口，將依賴關係的意識融入增強式學習模型中。LAUREL還採用了`移動'的概念，並引入了鏈鎖機制來管理動作的組合和龐大的動作空間。 我們實施了一個雙重獎勵函數來解決稀疏獎勵問題，並刪除無效的移動。為了配合雙重獎勵函數，我們提出了一種新的雙重獎勵蒙地卡羅增強式學習公式，這使得蒙地卡羅增強式學習在量子繞線中的搜索更加高效。 我們在各種基準電路上進行了廣泛的實驗，包括真實的量子算法電路，結果證明 LAUREL在優化電路深度的同時，與最先進的方法相比，同時保持了有競爭力的閘門數量。該研究還通過消融分析驗證了考慮量子運算依賴關係的有效性，並展示了該框架在更大規模的實際量子電路和量子設備上的可擴展性。結果顯示，LAUREL 在某些量子電路中，和之前同類型增強式學習研究中的結果相比下，在量子電路深度的開銷減少 92.6%，量子邏輯閘數量的開銷減少 93.0%。

This study presents LAUREL, a framework specifically designed to address the challenges of qubit routing, with the dual objectives of reducing both circuit depth and gate number of quantum circuits. LAUREL incorporates a dependency graph to model reinforcement learning(RL) states and enables exploration of different gate execution orders in equivalence quantum circuits. The framework creates a dependency-graph based lookahead window to incorporate dependency awareness into the RL model. It also adapts the concept of move and introduces a chain lock mechanism to manage both the action composition and the vast action space. A dual reward function is implemented to solve sparse reward issues and prune ineffective moves. To correspond with the dual reward function, we propose a new dual reward MCTS RL formulation, which makes the MCTS RL search more efficient in qubit routing. Our extensive experiments performed on diverse benchmarks, including well-known quantum algorithm circuits, demonstrate LAUREL's superiority in optimizing circuit depth while maintaining competitive gate numbers compared to state-of-the-art methods. The study also validates the efficacy of dependency-aware routing through an ablation analysis and demonstrates the framework's scalability for larger real quantum circuits and quantum devices. The results demonstrate that LAUREL can reduce the depth overhead of previous RL work by up to 92.6% and decrease the gate number overhead by as much as 93.0% in certain quantum circuits.