Factorized Boolean representations for efficient quantum synthesis

2026-08-27

AI Summary

该研究通过提取布尔表达式的代数结构来优化量子电路的合成，减少了控制计数和量子比特数量，从而提高了执行效率。

Abstract

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.

Problem

• quantum synthesis
• reversible circuits
• Boolean minimization
• control count
• factorized representation

Innovation

• Factorized Boolean Representations
• Control Count Reduction
• Quantum Circuit Synthesis
• Shared Factors Extraction
• Resource Optimization