自由费米子演化下费米子魔幻态的高效学习
Efficient Learning of Fermionic Magic States under Free-Fermion Evolution
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中文总结 AI 辅助
本文提出一种在未知自由费米子演化下高效学习费米子魔幻态的方法，利用粒子约化密度矩阵的谱结构重建块结构，以多项式复杂度实现高保真度恢复，并证明所需约化密度矩阵阶数在一般情况下是必要的。
中文摘要 AI 辅助
我们针对未知的粒子数守恒自由费米子演化下的一族费米子魔幻态建立了高效学习方案。每个输入块具有确定的粒子数，并且是福克态的叠加，其占据模式集在块内和块间均不相交。关键思想是利用粒子约化密度矩阵（RDMs）的谱结构，将单个块的贡献与涉及多个块的贡献分离开来，从而重建隐藏的块结构。对于每个块粒子数的固定上界，我们的算法使用单拷贝测量以及多项式样本和经典计算复杂度，以规定的保真度和高概率恢复状态的紧凑描述，无需事先了解块分解或演化。高达该上界的约化密度矩阵足以用于重建。我们进一步表明，这一约化密度矩阵阶数在一般情况下是必要的：该族中的两个正交状态在所有较低阶上可以具有相同的约化密度矩阵。这些结果表明，大量的非高斯块可以与高效的状态学习兼容。
英文摘要
We establish efficient learning for a family of fermionic magic states under unknown number-conserving free-fermion evolution. Each input block has a definite particle number and is a superposition of Fock states, with occupied mode sets disjoint both within and across blocks. The key idea is to exploit the spectral structure of particle reduced density matrices (RDMs) to separate contributions from individual blocks from those involving several blocks, allowing us to reconstruct the hidden block structure. For a fixed upper bound on the particle number per block, our algorithm uses single-copy measurements and polynomial sample and classical computational complexity to recover a compact description of the state with prescribed fidelity and high probability, without prior knowledge of the block decomposition or the evolution. RDMs up to this upper bound suffice for reconstruction. We further show that this RDM order is necessary in general: two orthogonal states in the family can have identical RDMs at every lower order. These results show that an extensive number of non-Gaussian blocks can be compatible with efficient state learning.
发表机构
- Graduate School of Quantum Science and Technology, Korea Advanced Institute of Science and Technology（韩国科学技术院量子科学与技术研究生院）
- School of Computational Sciences, Korea Advanced Institute of Science and Technology（韩国科学技术院计算科学学院）
- Department of Physics, Korea Advanced Institute of Science and Technology（韩国科学技术院物理系）
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