可达子空间上的精确对角补全：应用于QAOA布局
Exact Diagonal Completion on Reachable Subspaces: Application to QAOA Placement
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- University of Missouri（密苏里大学）
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中文总结 AI 辅助
本研究针对QAOA布局问题，提出在可达子空间上通过加权ℓ1优化实现精确对角补全，有效减少CX计数，但端到端优势未确立。
中文摘要 AI 辅助
未使用的编码状态为简化量子电路提供了机会。对于限制在可达子空间上的算法，可以在不改变理想计算的情况下优化未指定的对角算子条目。我们研究了应用于布局问题的量子近似优化算法（QAOA）的精确对角补全，使用保持置换的寄存器交换。我们通过Walsh系数的加权-ℓ1优化和平衡矩形上需要O(√m)项的稀疏递推来构造精确的曼哈顿距离算子，避免了O(m^4)的稠密约束存储。在160种几何形状中，加权-ℓ1补全在Gray码合成下，相对于四种替代扩展，在全部96个具有未使用二进制编码的案例中减少了受控非（CX）计数。在一个独立指定的60案例队列中，相对于虚拟坐标扩展的中位数减少在六个、九个和十二个位点分别为28.0%、53.9%和21.6%。在通用对角合成下，减少幅度降至10.9%、1.3%和0.7%，表明存在编译器依赖性。额外的辅助量子比特减少了混频器串行化，但令牌电路仍然比one-hot基线更深。理想布局模拟显示解决方案质量依赖于基线，经典搜索表现更好。OpenROAD集成将72个QAOA和216个经典布局通过时钟树综合和全局布线应用于六个RTL设计，且零溢出。补全改善了相位构造；未确立端到端优势。
英文摘要
Unused encoding states offer opportunities to simplify quantum circuits. For algorithms restricted to reachable subspaces, unspecified diagonal-operator entries can be optimized without changing ideal computation. We investigate exact diagonal completion for the quantum approximate optimization algorithm (QAOA) applied to placement, using permutation-preserving register swaps. We construct exact Manhattan-distance operators through weighted-$\ell_1$ optimization of Walsh coefficients and a sparse recurrence requiring $O(\sqrt{m})$ terms on balanced rectangles, avoiding $O(m^4)$ dense constraint storage. Across 160 geometries, weighted-$\ell_1$ completion reduces controlled-NOT (CX) counts relative to four alternative extensions in all 96 cases with unused binary codes under Gray-code synthesis. On an independently specified 60-case cohort, median reductions relative to virtual-coordinate extension are 28.0\%, 53.9\%, and 21.6\% at six, nine, and twelve sites. Under generic diagonal synthesis, reductions decrease to 10.9\%, 1.3\%, and 0.7\%, demonstrating compiler dependence. Additional ancillas reduce mixer serialization, but token circuits remain deeper than one-hot baselines. Ideal placement simulations show baseline-dependent solution quality, with classical search performing better. OpenROAD integration takes 72 QAOA and 216 classical placements across six RTL designs through clock-tree synthesis and global routing with zero overflow. Completion improves phase construction; no end-to-end advantage is established.
