用于高效量子综合的因式分解布尔表示
Factorized Boolean representations for efficient quantum synthesis
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中文总结 AI 辅助
该研究提出因式分解布尔表示，突破传统逻辑最小化的局限，通过提取布尔表达式的共享因子优化量子综合，在减少量子比特数的同时降低超线性控制成本，提升电路执行效率。
中文摘要 AI 辅助
量子算法有望带来超越经典计算的优势，但在纠错硬件上运行它们需要将布尔规范转换为可逆电路，而这种转换所需的资源决定了哪些内容可执行。现有方法会最小化布尔表达式并将其映射到电路，假设最小化形式是最优的。本文表明，最小化表达式保留了最小化过程无法触及的代数结构，这些结构源于其项之间的包含和互补极性关系，提取这些结构可得到更易执行的电路，尽管其操作更多。关键指标不是电路的操作数，而是其最宽操作的控制数，这是一种超线性成本；提取共享因子会用少量宽操作换取大量窄操作，并减少量子比特数。在量子搜索和因式分解算法的基准及预言机上，该变换在表示层面从未增加这两种成本指标，这是其构造带来的保证。转换为可执行电路会损失部分优势，因为辅助线路必须被反计算，但因式分解电路仍使领先的电路级优化器达到了更低的最终计数，且比无辅助时更快。因此，计算的表示本身就是一种资源，可在编译前优化，且与逻辑最小化和电路级优化均不同。
英文摘要
Quantum algorithms promise advantages beyond classical reach, but running them on error-corrected hardware requires translating Boolean specifications into reversible circuits, and the resources that translation demands determine what is executable. Established methods minimize a Boolean expression and map it to a circuit, assuming the minimized form is best. Here we show that minimized expressions retain algebraic structure minimization cannot reach, arising from containment and complementary-polarity relationships among their terms, and that extracting it yields circuits cheaper to execute despite having more operations. The decisive quantity is not a circuit's operation count but the control count of its widest operation, a superlinear cost; extracting shared factors trades a few wide operations for many narrow ones and reduces qubit count. Across benchmarks and oracles from quantum search and factoring algorithms, at the representation level the transformation never increases either cost measure, a guarantee from its construction. Translation to an executable circuit returns part of that advantage, since auxiliary lines must be uncomputed, yet the factorized circuit still left a leading circuit-level optimizer reaching lower final counts, and faster, than unaided. The representation of a computation is therefore itself a resource, optimizable before compilation and distinct from both logic minimization and circuit-level optimization.
发表机构
- Portland State University（波特兰州立大学）
机构由 AI 辅助整理，请以论文原文为准。
