DeComp2：描述复杂度感知分解
DeComp2: Description Complexity aware Decomposition
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中文总结 AI 辅助
该研究提出将电路复杂度与发射电路的描述复杂度配对，最小化加法总和以提升编译器目标到生命周期复杂度。通过基于压缩代理的穷举HT枚举实例化目标，实验表明两代理与电路复杂度正相关但打破秩次顺序，促使将描述复杂度作为编译器中间表示的优化信号。
中文摘要 AI 辅助
量子编译器优化诸如门数量、深度和保真度等仅执行代理，将编译后的电路视为成本单元。这混淆了两种不同资源，即运行时基板的工作量和描述要做什么所需的信息量。展开循环程序会使运行时成本不变，但会消除下游优化和重用所依赖的层次结构。我们提出通过将电路复杂度$\mathcal{C}_{\mathrm{circ}}$与发射电路的柯尔莫哥洛夫风格描述复杂度$\mathcal{C}_{\mathrm{Kol}}$配对，并最小化加法总和$\mathcal{C}_{\mathrm{tot}} = \alpha\,\mathcal{C}_{\mathrm{circ}} + \beta\,\mathcal{C}_{\mathrm{Kol}}$，将编译器目标从执行提升到生命周期复杂度。这反映了量子复杂度第二定律的加法位置和动力学熵，并作为对否则退化的$\mathcal{C}_{\mathrm{circ}}$最小化器集合的最小描述长度正则化器。我们通过基于压缩代理的穷举HT枚举在$SU(2)$上实例化目标，该代理上界$\mathcal{C}_{\mathrm{Kol}}$。在哈尔代表性目标网格上进行实验，两个代理与$\mathcal{C}_{\mathrm{circ}}$正相关，但在相当一部分点上打破了其秩次顺序，排除了紧密的函数依赖。通过校准权重，联合成本为一小部分但具有操作意义的目标选择了一个在$\varepsilon$球中既不是最短也不是最可压缩的HT字符串的候选者，展示了仅基于$\mathcal{C}_{\mathrm{circ}}$的优化器丢弃的编译选择，并促使将$\mathcal{C}_{\mathrm{Kol}}$作为编译器层次中间表示的主动优化信号。
英文摘要
Quantum compilers optimize execution-only proxies such as gate count, depth, and fidelity, treating the compiled circuit as the unit of cost. This conflates two distinct resources, how much the substrate has to do at run time, and how much has to be said to describe what to do. Unrolling a looped program leaves run-time cost unchanged while erasing the hierarchical structure on which downstream optimization and reuse rely. We propose lifting the compiler objective from execution to life cycle complexity by pairing the circuit complexity $\mathcal{C}_{\mathrm{circ}}$ with a Kolmogorov-style description complexity $\mathcal{C}_{\mathrm{Kol}}$ of the emitted circuit, and minimizing the additive total $\mathcal{C}_{\mathrm{tot}} = α\,\mathcal{C}_{\mathrm{circ}} + β\,\mathcal{C}_{\mathrm{Kol}}$. The mirrors the additive positional and kinetic entropy of the second law of quantum complexity, and reads as a minimum-description-length regularizer over the otherwise degenerate set of $\mathcal{C}_{\mathrm{circ}}$-minimizers. We instantiate the objective on $SU(2)$ through exhaustive HT-enumeration with compression-based surrogates upper-bounding $\mathcal{C}_{\mathrm{Kol}}$. Across a Haar-representative target grid the two surrogates correlate positively with $\mathcal{C}_{\mathrm{circ}}$ yet break its rank order on a non-trivial fraction of points, ruling out a tight functional dependence. With calibrated weights the joint cost selects, for a small but operationally meaningful fraction of targets, a candidate that is neither the shortest nor the most compressible HT-string in the $\varepsilon$-ball, exhibiting the compilation choices a $\mathcal{C}_{\mathrm{circ}}$-only optimizer discards and motivating $\mathcal{C}_{\mathrm{Kol}}$ as an active optimization signal for hierarchical intermediate representation for compiler.
