基态的低拷贝学习

中文摘要 AI 辅助

探测基态的多重属性是理解量子物质的核心，然而传统的读出方式可能代价高昂，因为它需要消耗大量独立制备的拷贝。在此，在拷贝稀缺（copy-scarce）的体制下，我们建立了初始基态拷贝数量与所需哈密顿量演化时间之间的最优权衡关系，用于估计多个可观测量或重构唯一带隙基态的完整经典描述。我们推导出一个统一不等式，量化了即使所有拷贝可能被消耗，利用初始拷贝和受控动力学区分基态的能力。该不等式给出了任何协议执行任一任务所必须消耗的最坏情况哈密顿量时间下界。我们构建了并行催化读出方案，该方案几乎不变地返回所有初始拷贝，同时达到这些下界（相差多对数因子）。我们的协议不需要相干制备电路或其逆电路，且其哈密顿量演化时间仅依赖于期望返回误差的倒数的对数。因此，最优的拷贝-动力学权衡可以与催化返回同时实现。数值基准进一步表明，即使在乐观的制备成本模型下，相对于任务专用的拷贝消耗协议，端到端的哈密顿量演化时间也大幅减少。我们的结果揭示了一个拷贝-动力学资源图谱，将拷贝稀缺学习与由已知的阴影层析和纯态层析协议实现的纯拷贝端点联系起来。

英文摘要

Probing multiple properties of ground states is central to understanding quantum matter, yet conventional readout can be prohibitively costly because it consumes many independently prepared copies. Here, in copy-scarce regimes, we establish optimal trade-offs between the number of initial ground-state copies and elapsed Hamiltonian-evolution time required for estimating multiple observables or reconstructing a full classical description of a unique gapped ground state. We derive a unifying inequality that quantifies how well ground states can be distinguished using initial copies and controlled dynamics, even when all copies may be consumed. It yields worst-case lower bounds on elapsed Hamiltonian time that any protocol must incur to perform either task. We construct parallel catalytic readouts that return all initial copies nearly unchanged while attaining these bounds up to poly-logarithmic factors. Our protocols require no coherent preparation circuit or its inverse, and their elapsed Hamiltonian time depends only logarithmically on the inverse of the desired return error. Thus, optimal copy--dynamics trade-offs can be attained together with catalytic return. Numerical benchmarks further show substantial reductions in end-to-end elapsed Hamiltonian time relative to a task-specialized copy-consuming protocol, even under an optimistic preparation-cost model. Our results reveal a copy--dynamics resource landscape connecting copy-scarce learning to copy-only endpoints realized by known protocols for shadow tomography and pure-state tomography.

发表机构

• University of Tokyo（东京大学）
• Keio University（庆应义塾大学）

机构由 AI 辅助整理，请以论文原文为准。