发表机构
Freie Universität Berlin; Humboldt-Universität zu Berlin; Okinawa Institute of Science and Technology Graduate University; Max-Born-Institut; Helmholtz-Zentrum Berlin für Materialien und Energie（柏林自由大学; 柏林洪堡大学; 冲绳科学技术大学院大学; 马克斯·玻恩研究所; 亥姆霍兹柏林材料与能源中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用恒星秩形式化方法，分析光子催化协议在生成压缩猫态中的最优性，并量化非高斯资源复杂度、保真度与损耗之间的权衡。
AI 中文摘要
非高斯量子态和操作是实现玻色子平台上量子计算优势和量子纠错的关键资源。然而，在光学环境中生成它们仍然是一项具有挑战性的实验任务，通常依赖于概率性 heralded 协议。本文深入分析了低数 Fock 态与压缩态之间的光子催化在生成压缩相干态叠加中的适用性。我们采用恒星秩形式化来表征输入资源（包括态和测量）以及生成态的非高斯复杂度。这使得我们能够系统比较催化输出与目标态之间的保真度，以及任何使用相同非高斯输入资源的协议所能达到的最大保真度。在此意义上，我们识别了所考虑的催化协议被证明是最优的实例。我们确定了可以用最少资源实现目标态高保真近似的参数区域。此外，我们以成功概率和态质量为基准，将光子催化与受高斯玻色采样启发的协议进行比较，突出了确定性 Fock 态源的优势。我们还研究了相关非高斯资源的生成，包括与量子纠错相关的压缩 Fock 态。为了考虑实验不完美性，我们使用 Fock 基中的希尔伯特空间截断方法对所有光学模式中的损耗进行建模，并分析了生成态在现实条件下的鲁棒性。我们的结果量化了光子催化协议中非高斯资源复杂度、可达保真度和损耗之间的权衡，为近期光子实现提供了实用指南。
英文摘要
Non-Gaussian quantum states and operations constitute essential resources for achieving quantum computational advantage and enabling quantum error correction in bosonic platforms. However, their generation in optical settings remains a challenging experimental task, often relying on probabilistic heralded protocols. Here, we present an in-depth analysis of the suitability of photon catalysis between low number Fock states and squeezed states for the generation of squeezed coherent state superpositions. We employ the stellar rank formalism to characterize the non-Gaussian complexity of input resources (including both states and measurements) and the generated states. This enables a systematic comparison of the fidelity between the catalyzed output and the target states to the maximum fidelity achievable by any protocol with the same non-Gaussian input resources. In this sense, we identify instances where the catalysis protocols considered here are provably optimal. We identify parameter regimes in which high-fidelity approximations of the target states can be achieved with minimal resources. Furthermore, we benchmark the performance of photon catalysis against Gaussian boson sampling-inspired protocols in terms of success probability and state quality, highlighting the advantages of deterministic Fock state sources. We also investigate the generation of related non-Gaussian resources including squeezed Fock states, relevant for quantum error correction. To account for experimental imperfections, we model losses across all optical modes using a Hilbert space truncation approach in the Fock basis and analyze the robustness of the generated states under realistic conditions. Our results quantify the trade-offs between non-Gaussian resource complexity, achievable fidelity, and losses in photon catalysis protocols, providing practical guidelines for near-term photonic implementations.
Comments25 pages, 19 figures
