发表机构
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用开放量子系统技术，识别小维度李群以避免指数级大群，实现高效态制备和通道普适性，并揭示廉价与昂贵态的景观。
AI 中文摘要
我们提出了一种新颖的态制备方法，通过充分利用开放量子系统的全部能力。我们不再处理$n$量子比特上的整个酉群，而是识别出$(n+3)$量子比特上的一个小李群$G$。其李代数的维度为$\text{poly}(n)$。从任意固定输入态出发，通过反复使用部分迹和环境中的态制备以及群操作，可以逼近任意态。此外，我们还识别出一个单一的（开放系统魔法）相互作用哈密顿量，其酉群可以与上述开放量子系统技术结合，实现在所有密度矩阵空间上的传递性。类似地，我们证明了通过使用更大的环境，可以逼近$n$量子比特上的所有通道，实现通道普适性。我们识别出的有趣小群源自局部泡利字符串的李代数，并导致了一个新的关于廉价和昂贵态、密度矩阵和通道的景观。
英文摘要
We propose a novel approach to state preparation by embracing the full power of open quantum systems. Instead of working with the whole unitary group in $n$ qubits, we identify a small Lie group $G$ in $(n+3)$ qubits. The dimension of its Lie algebra is $\text{poly}(n)$. Every state can be approximated starting from any fixed input state by repeatedly using partial trace and state preparation in the environment alongside group operations. Moreover, we also identify a single (open system magic) interaction Hamiltonian whose unitary group can be combined with open system quantum technology mentioned above to achieve transitivity on the space of all densities. Similarly, we show that all channels on $n$ qubits can be approximated by using a larger environment, achieving channel universality. The interesting small groups we identify are derived from Lie algebras of local Pauli strings and lead to a new landscape of cheap and expensive states, densities, and channels.
