AI 中文总结
研究无源线性光学中经典模拟与模型集中问题，基于表示理论框架，通过分析粒子数守恒可观测量投影及渐近缩放表征期望值集中，关联经典模拟技术，确定可训练可观测量类别，找到部分避免指数集中且超出经典模拟的情况。
AI 中文摘要
无源线性光学是量子计算的一种受限模型，在采样任务中有量子优势的复杂性理论证据且损耗低，对近期算法有吸引力。在量子比特架构中，大量工作揭示了贫瘠高原与经典可模拟性之间的紧密联系。对于玻色子系统是否存在类似权衡很大程度上未被探索。基于最近为随机无源线性光学电路的矩开发的表示理论框架，我们通过评估相关粒子数守恒可观测量族到酉群不可约表示的投影并分析其渐近缩放来表征期望值的集中情况。我们表明集中由输入态和可观测量到不可约表示的投影的不对准决定，在玻色子环境中给出了广义纠缠和局域性的统一表示理论解释。我们进一步将这些集中性质与现有经典模拟技术相关联，确定了允许有效经典模拟的可训练可观测量的广泛类别。相反，我们确定了福克态输入和可观测量，它们似乎避免指数集中，同时保留了已知有效经典模拟方法无法访问的多项式大信号分量。这种分离只是部分的：大部分信号在经典上仍然易于处理，剩余部分虽然没有被指数抑制，但足够小以至于截断可以作为具有多项式小误差的经典替代。我们的框架仍然为寻找明确结合不存在指数集中且超出已知有效经典模拟方法的区域提供了一条系统途径。
英文摘要
Passive linear optics is a restricted model of quantum computation, with complexity-theoretic evidence of quantum advantage for sampling tasks and low losses that make it attractive for near-term algorithms. In qubit architectures, a body of work has revealed a close connection between barren plateaus and classical simulability. Whether an analogous tradeoff exists for bosonic systems remains largely unexplored. Building on a recently developed representation-theoretic framework for moments of random passive linear-optical circuits, we characterize the concentration of expectation values for relevant families of particle-number-preserving observables by evaluating their projections into irreducible representations of the unitary group and analyzing their asymptotic scaling. We show that concentration is governed by the misalignment of the projections into irreducible representations of the input state and the observable, giving a unified representation-theoretic interpretation of generalized entanglement and locality in the bosonic setting. We further relate these concentration properties to existing classical simulation techniques, identifying broad classes of trainable observables that admit efficient classical simulation. Conversely, we identify Fock-state inputs and observables that appear to evade exponential concentration while retaining a polynomially large signal component not accessible to known efficient classical simulation methods. The separation is only partial: most of the signal remains classically tractable, and the residual part, while not exponentially suppressed, is small enough that a truncation serves as a classical surrogate with polynomially small error. Our framework nonetheless provides a systematic route for searching for regimes that unambiguously combine the absence of exponential concentration and lies beyond known efficient classical simulation methods.
