量子纠缠分配的样本复杂度
The Sample Complexity of Quantum Entanglement Allocation
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- Stanford University（斯坦福大学）
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中文总结 AI 辅助
本研究分析量子纠缠分配中的样本复杂度，提出基于固定探测器的编码方法，刻画预测对比区域，并在量子设备与零售数据上验证了方法的有效性。
中文摘要 AI 辅助
需要多少过去的请求才能决定哪些量子比特应共享纠缠？我们表明，答案取决于查询所产生的分配选择：更大的记忆可能不需要更多数据。记忆存储一个经典比特，并通过一个固定的探测器来响应请求，该探测器在每个测量扇区内保持相干性。对于独立的对易 $X$-型和 $Z$-型泡利查询，我们刻画了完全可达到的预测对比区域，并构造了在每个非零顶点处保持该比特的编码。在尖锐报告下，一个 $d$ 量子比特路径和最多 $k$ 个量子比特的组，在 $m$ 次请求后的极小极大超额误差正比于 $k^{-1}\min\{1,\sqrt{d\log(k+1)/m}\}$，对 $2\leq k<d$ 一致成立。当深度、区域数量和每个区域的连接数保持有界时，连通双团区域可以增长而不增加样本需求。制备噪声引入了单独的校准要求。我们推导出与额外新鲜探测器调用之间的精确权衡，并将学习规律转移到结构化交易共置中。总体风险实验测试了统计预测。我们还在原生 15 量子比特设备上比较了编码，并在公开购买篮子上比较了学习到的分区。完整链在设备上获胜；频率分组在最大容量零售场景中优于篮子搜索。
英文摘要
How many past requests are needed to decide which qubits should share entanglement? We show that the answer depends on the allocation choices created by the queries: a larger memory can require no more data. The memory stores a classical bit and answers requests through a fixed detector that preserves coherence within each measured sector. For independent commuting $X$- and $Z$-type Pauli queries, we characterize the full attainable prediction-contrast region and construct encodings that preserve the bit at every nonzero vertex. With sharp reports, a $d$-qubit path and groups of at most $k$ qubits have minimax excess error after $m$ requests proportional to $k^{-1}\min\{1,\sqrt{d\log(k+1)/m}\}$, uniformly for $2\leq k<d$. Connected biclique regions can grow without increasing sample demand when depth, region count and connections per region stay bounded. Preparation noise introduces a separate calibration requirement. We derive an exact tradeoff with extra fresh detector calls and transfer the learning law to structured transaction co-location. Population-risk experiments test the statistical predictions. We also compare encodings on a native 15-qubit device and learned partitions on public purchase baskets. The full chain wins on the device; frequency grouping outperforms basket search in the largest-capacity retail setting.
