AI 中文总结
本研究提出确定性单参数协议，将无穷维希尔伯特空间福克态制备映射为二维振幅放大，实现具有$n^{1/4}$电路深度的精确高保真福克态制备，还可推广至态转移、纠缠态等多种玻色量子态制备。
AI 中文摘要
高效、确定性且高保真的大尺度福克态制备，对推动玻色量子技术规模化发展以及探索高激发能下的量子现象至关重要。我们提出了一种确定性单参数（D1p）协议，将无穷维希尔伯特空间中的福克态制备映射为二维振幅放大。从振幅为$|α|\simeq\sqrt{n}$的相干态出发，初始目标态布居数的标度关系为$n^{-1/2}$，由此得到的迭代次数与电路深度为$\mathcal{O}(n^{1/4})$。相位匹配可保证理想模型下的保真度为1；值得注意的是，制备$|{10^6}\rangle$仅需39次迭代。该协议仅使用位移操作和数选择相位操作，无需数值优化，还可进一步推广至态转移、一般叠加态、有限维系统以及多体纠缠态的制备。在大振幅区域，其多目标形式可制备$L$条腿的猫态，迭代次数仅由$L$决定；多达十条腿的猫态仅需两次迭代即可制备，且与相干态振幅无关。该框架为在支持这些基础操控的平台上制备高激发玻色态提供了一条具有广泛适用性的途径。
英文摘要
Efficient, deterministic, and high-fidelity preparation of large Fock states is essential for scaling bosonic quantum technologies and exploring quantum phenomena at large excitation energies. We introduce a deterministic one-parameter (D1p) protocol that maps Fock-state preparation in an infinite-dimensional Hilbert space onto two-dimensional amplitude amplification. Starting from a coherent state with $|α|\simeq\sqrt{n}$, the initial target-state population scales as $n^{-1/2}$, yielding an iteration count and circuit depth of $\mathcal{O}(n^{1/4})$. Phase matching guarantees unit fidelity in the ideal model; remarkably, preparing $|{10^6}\rangle$ requires only 39 iterations. The protocol uses only displacements and number-selective phase operations, requires no numerical optimization, and further extends to state transfer, general superpositions, finite-dimensional systems, and multipartite entangled states. In the large-amplitude regime, its multi-target form prepares $L$-legged cat states with an iteration count determined only by $L$; cats with up to ten legs require only two iterations, independent of the coherent-state amplitude. This framework provides a broadly applicable route to highly excited bosonic states on platforms supporting these elementary controls.
Comments8 pages, 3 figures
