ZX演算优化用于Solovay-Kitaev量子电路合成的数值评估
Numerical Evaluation of ZX Calculus Optimization for Solovay Kitaev Quantum Circuit Synthesis
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中文总结 AI 辅助
本研究通过数值评估发现，对Solovay-Kitaev算法合成的量子电路冗余进行ZX演算图示后处理，可减少26.6%-30.1%总门数及18.5%-22.2% T门数，且不改变近似误差，但编译成本随递归深度急剧上升。
中文摘要 AI 辅助
容错架构通过魔法态蒸馏实现非Clifford T门，因此合成电路的T门计数决定了其物理成本。Solovay-Kitaev算法从有限门集合近似任意单量子比特幺正算子，其序列长度仅随目标误差的倒数呈多项式对数增长，但该算法优化的是数值收敛性而非电路经济性，且其输出存在门级编译器无法识别的结构冗余。本文报告了对该冗余可通过图示后处理恢复程度的测量结果：我们合成了1200个随机单量子比特目标，涵盖三个Pauli旋转族及通用门U(θ,φ,λ)，在Clifford+T门集上以三个递归深度进行合成，转换为类图ZX图，通过自动重写简化后再提取为电路。后处理可减少总门数的26.6%-30.1%及T门数的18.5%-22.2%。绝对节省量随递归深度增加，从约60门增至约1600门，但相对节省量则不随深度变化：其从最浅设置略有上升后，在电路长度25倍的变化范围内保持平稳，且在最深设置下，四个目标族彼此不再可区分。由于重写规则保留了所实现的线性映射，近似误差保持不变；相比之下，重写层的编译时间成本随深度急剧增长，最终超过合成本身的成本。
英文摘要
Fault-tolerant architectures implement non-Clifford T gates through magic-state distillation, so the T-count of a synthesized circuit dominates its physical cost. The Solovay-Kitaev algorithm approximates any single-qubit unitary from a finite gate set with a sequence length that grows only polylogarithmically in the inverse target error, but it optimizes for numerical convergence rather than circuit economy, and its output carries structural redundancy that a gate-level compiler cannot see. We report a measurement of what diagrammatic post-processing recovers from that redundancy. Twelve hundred random single-qubit targets, spanning the three Pauli rotation families and the general gate U(theta, phi, lambda), are synthesized over Clifford+T at three recursion depths, translated into graph-like ZX-diagrams, simplified by automated rewriting, and extracted back to circuits. Post-processing removes 26.6-30.1% of the total gate count and 18.5-22.2% of the T-count. The absolute saving grows with recursion depth, from about 60 to about 1600 gates, while the fractional saving does not: it rises slightly from the shallowest setting and is then flat across a twenty-five-fold change in circuit length, and by the deepest setting the four target families are no longer distinguishable from one another. Because the rewrite rules preserve the implemented linear map, the approximation error is unchanged. The compile-time cost of the rewriting layer, by contrast, grows sharply with depth and comes to dominate the synthesis itself.
