具有可忽略超额开销的精确虚拟信道编程
Exact Virtual Channel Programming with Vanishing Excess Overhead
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中文总结 AI 辅助
该研究针对有限维物理处理器无法精确编程连续酉信道的问题，构造了与目标无关的精确重构协议，证明了采样开销与系统维度的二次关系及超额开销随Choi程序数反比消失的规律，明确了量子程序内存与经典采样的量化权衡。
中文摘要 AI 辅助
有限维物理处理器无法精确编程连续族的不同酉信道。我们表明，当目标信道存储在归一化Choi态中，且其输出可观测量通过对物理信道进行采样并对测量结果进行经典后处理来重构时，这种阻碍会呈现量化形式。对于任意d维信道，我们构造了与目标无关的精确重构协议，并证明了最优单副本采样开销随系统维度呈二次增长。我们进一步证明了固定d下的严格定律：超额开销随相同Choi程序的数量呈反比消失。该上界结合了确定性基于端口的隐形传态与准分解，以校正其去极化失真。逆命题将任何低开销重构协议映射为未知酉的物理学习器，并利用局域量子估计恢复相同主导系数。这些结果将通用无编程阻碍重新表述为量子程序内存与经典采样之间的量化权衡，其主导成本反映了可局域学习的酉自由度。
英文摘要
A finite-dimensional physical processor cannot exactly program a continuous family of distinct unitary channels. We show that this obstruction becomes quantitative when the target channel is stored in a normalized Choi state and its output observables are reconstructed by sampling physical channels and classically post-processing their measurement outcomes. For arbitrary $d$-dimensional channels, we construct a target-independent exact reconstruction protocol and prove the optimal one-copy sampling overhead, which grows quadratically with system dimension. We further prove the sharp fixed-$d$ law that the excess overhead vanishes inversely with the number of identical Choi programs. The upper bound combines deterministic port-based teleportation with a quasi-decomposition that corrects its depolarizing distortion. The converse maps any low-overhead reconstruction protocol to a physical learner of unknown unitaries and uses local quantum estimation to recover the same leading coefficient. These results recast the universal no-programming obstruction as a quantitative trade-off between quantum program memory and classical sampling, with a leading cost that reflects the locally learnable unitary degrees of freedom.
发表机构
- The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
- QudeLeap Research（量子跃迁研究）
机构由 AI 辅助整理，请以论文原文为准。
