AI 中文总结
该研究针对量子电路成本高的问题，提出基于矩形覆盖的ESOP表达式因式分解算法，经基准测试可降低经典电路文字数和量子电路Maslov成本20%-95%。
AI 中文摘要
当前量子电路的实现成本极高，尤其因大量使用Toffoli门所致。因此，随着表达式愈发复杂，通过因式分解来优化电路成本至关重要。在提出的ESOP表达式因式分解算法中，每个乘积项被转换为二维矩阵中的一个单元，利用不相交矩形覆盖和奇偶矩形覆盖方法确定最优的因式分解AND/EXOR解。采用两个Python程序实现这些算法，并使用知名基准进行测试评估。结果显示，根据表达式规模的不同，经典逻辑电路的文字数量和量子电路的Maslov成本均降低了20%-95%。
英文摘要
The implementation of quantum circuits is currently very expensive, especially due to the usage of large Toffoli gates. Therefore, it is critical to optimize circuit costs by factoring expressions as they become more complex. In the proposed algorithms to factor ESOP expressions, each product term is converted into a cell in a 2D matrix, and optimal factored AND/EXOR solutions are determined using Disjoint and Even-Odd Rectangle covering methods. Two Python programs implementing these algorithms were tested and evaluated using well-known benchmarks. The results showed that both the literal counts used in classical logic circuits as well as the Maslov cost used in quantum circuits was reduced by 20%-95% depending on expression size.
