基于二元决策图的大语言模型驱动量子电路合成算法设计
LLM-Driven Algorithm Design for Quantum Circuit Synthesis based on Binary Decision Diagrams
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- KAIST（韩国科学技术院）
- Radical Numerics
- Omelet Inc（Omelet公司）
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中文总结 AI 辅助
该研究提出基于LLM的进化框架\texttt{QuantumEvo}，发现启发式HGA-QE优化BDD变量排序，使合成量子电路的QCC性能提升，在基准测试中表现出竞争力。
中文摘要 AI 辅助
量子电路是在量子设备上实现量子算法的核心，其中量子门必须是可逆的。许多量子算法依赖于布尔函数，因此这些布尔函数必须在量子电路中被可逆地实现。可逆电路合成提供了一种将此类布尔函数转换为可逆电路的方法。二元决策图（Binary Decision Diagrams，简称BDD）为该任务提供了一种可扩展的方法，但生成的BDD和电路高度依赖于变量排序。现有的排序启发式方法通常会最小化BDD的大小，因为BDD大小与电路大小密切相关。然而，BDD大小是合成电路量子成本（Quantum Cost of the Synthesized Circuit，简称QCC）的不完美替代指标。我们提出了\texttt{QuantumEvo}，这是一个使用大语言模型（LLM）作为QCC感知型BDD变量排序启发式生成器的进化框架。\texttt{QuantumEvo}并非直接预测排序，而是在从多个启发式族初始化的排序启发式中进行搜索。候选启发式通过标准BDD操作直接操纵变量排序，并由下游QCC进行选择。所发现的启发式HGA-QE修改了遗传算法内部的筛选步骤，使该过程与QCC更好地对齐。在基准测试集上，HGA-QE相对于每个函数的最佳基线实现了70.9%的平局或胜率，并且在13.5%的函数上是严格最优的。结果表明HGA-QE具有广泛的竞争力，在来自启发式发现所用数据之外的两个基准测试套件中，HGA-QE在严格获胜方面表现出更明显的相对优势。
英文摘要
Quantum circuits are central to implementing quantum algorithms on quantum devices, where quantum gates must be reversible. Many quantum algorithms rely on Boolean functions, which must therefore be implemented reversibly within quantum circuits. Reversible circuit synthesis provides a way to translate such Boolean functions into reversible circuits. Binary decision diagrams (BDDs) offer a scalable approach to this task, but the resulting BDDs and circuits depend heavily on variable ordering. Existing ordering heuristics commonly minimize BDD size because it is closely tied to the circuit size. However, BDD size is an imperfect proxy for the quantum cost of the synthesized circuit (QCC). We propose \texttt{QuantumEvo}, an evolutionary framework that uses an LLM as a heuristic generator for QCC-aware BDD variable ordering. Instead of predicting orderings directly, \texttt{QuantumEvo} searches over ordering heuristics initialized from multiple heuristic families. Candidate heuristics directly manipulate variable orderings using standard BDD operations and are selected by downstream QCC. The discovered heuristic, HGA-QE, modifies the sifting step inside a genetic algorithm so that the procedure is better aligned with QCC. Across the benchmark set, HGA-QE achieves a 70.9\% tie-or-win rate against the per-function best baseline and is strictly best on 13.5\% of the functions. The results demonstrate broadly competitive QCC performance, with HGA-QE showing a clearer relative advantage in strict wins on the two benchmark suites drawn from sources different from the data used for heuristic discovery.
