虚拟蒸馏成功概率的斯莱皮恩界
Slepian Bounds on the Success Probability of Virtual Distillation
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中文总结 AI 辅助
该研究针对虚拟蒸馏的成功概率，推导了由变分带和结果窗口构建的斯莱皮恩集中算子主导本征值给出的渐近成功概率界，还通过噪声QAOA对2-正则最大割的计算验证了相关改进与失效模式。
中文摘要 AI 辅助
虚拟蒸馏是一种强大的近期误差缓解基础原语，但它也是一种频谱滤波器：它会放大噪声密度矩阵中已存在的主导本征向量分量。我们证明，对于有限带变分态，这种滤波无法在一组被接受的测量结果内部产生新的集中度。蒸馏后的渐近成功概率受斯莱皮恩集中算子的主导本征值约束，该算子由指定的变分带和该结果窗口构建。此外，稳健高成功谱分量的数量受限于斯莱皮恩活动维度。对于比特串结果窗口，显式沃尔什带实现具有布尔超立方体上的克拉夫楚克核。针对2-正则最大割的有限尺寸噪声量子近似优化算法（QAOA）计算，既说明了带内改进，也说明了分支解析结果预测的带外失效模式。
英文摘要
Virtual distillation is a powerful near-term error-mitigation primitive, but it is also a spectral filter: it amplifies the dominant eigenvector component already present in the noisy density matrix. We show that, for a finite-band variational state, this filtering cannot create new concentration inside a set of accepted measurement outcomes. The asymptotic success probability after distillation is bounded by the leading eigenvalue of a Slepian concentration operator built from a specified variational band and that outcome window. Moreover, the number of robust high-success spectral components is limited by the Slepian active dimension. \rev{For bit-string outcome windows, an explicit Walsh-band realization has a Krawtchouk kernel on the Boolean hypercube. Finite-size noisy-QAOA calculations for 2-regular Max-Cut illustrate both the in-band improvement and the out-of-band failure modes predicted by the branch-resolved result.
