基于X-Map决策图的Oracle综合

中文摘要 AI 辅助

量子Oracle作为可逆的黑盒算子，将经典布尔函数编码到量子态中，使得在量子叠加态中实现高效的函数评估成为可能。Oracle实现的资源效率对众多量子算法的性能至关重要。最先进的Oracle综合方法大多依赖于紧凑的布尔函数表示，如异或和之积（ESOP），但在处理大规模函数时仍面临过高的$T$-计数和$CX$-计数问题。本文提出了一种新颖的紧凑表示方法，名为X-Map决策图（XMDD），用于布尔函数，该方法整合了局部可逆映射和互补边以实现更高的压缩效率。基于XMDD，我们进一步开发了一种优化的量子Oracle综合算法。大量实验结果表明，对于输入变量超过七个的布尔函数，我们的方法在几乎所有测试用例中均优于最先进的基于ESOP的方法和Qiskit，同时实现$T$-计数和$CX$-计数的降低，且无明显权衡。此外，我们展示了通过采用更优的变量排序可以进一步提升性能。所提出的基于XMDD的框架为近期和容错量子计算中的实际Oracle综合提供了一种可扩展且资源高效的解决方案。

英文摘要

Quantum oracles act as reversible black-box operators that encode classical Boolean functions into quantum states, enabling efficient function evaluation in quantum superposition. The resource efficiency of oracle implementation is critical to the performance of numerous quantum algorithms. Most state-of-the-art oracle synthesis approaches rely on compact Boolean function representations such as exclusive-sum-of-products (ESOP), yet still suffer from excessive $T$-count and $CX$-count for large-scale functions. In this paper, we propose a novel compact representation named X-Map decision diagram (XMDD) for Boolean functions, which integrates local invertible maps and complement edges to achieve higher compression efficiency. Based on XMDD, we further develop an optimized quantum oracle synthesis algorithm. Extensive experimental results demonstrate that, for Boolean functions with more than seven input variables, our method outperforms the state-of-the-art ESOP-based approach and Qiskit in nearly all test cases, achieving simultaneous reduction in both $T$-count and $CX$-count without an obvious trade-off. Moreover, we show that the performance can be further boosted by employing more optimal variable orderings. The proposed XMDD-based framework provides a scalable and resource-efficient solution for practical oracle synthesis in near-term and fault-tolerant quantum computing.

发表机构

• Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）
• Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
• Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息中心）

机构由 AI 辅助整理，请以论文原文为准。