AI 中文总结
该研究以魔术态为量子生成式建模资源，建立基于概率单纯形的评估框架，发现 IQP 电路能高效消耗魔术态，是量子优势演示的有前景候选。
AI 中文摘要
量子生成式建模将采样视为生成任务：训练参数化量子电路，使其采样结果重现目标概率分布。瞬时量子多项式时间（IQP）电路兼具结构简洁性与量子优势的复杂性理论证据，但其实用价值不仅取决于表达能力，还依赖于消耗真正量子资源的效率。我们以魔术态（magic，即非 Stabilizer 态）作为量子生成式建模的资源来研究该问题。我们发现，投影希尔伯特空间中基于保真度和测地线的计算进展概念不适用于生成式模型，因为操作性能由输出概率分布而非量子态本身决定。我们在概率单纯形上直接评估魔术态消耗，用 Jensen-Shannon 散度的变化量化进展。将该框架应用于训练后的随机 γ-稀疏 IQP 电路，显示出高效魔术态使用的特征，主要贡献来自两量子比特门。由于 IQP 电路产生的中间魔术态远低于具有相同采样分布的相位随机化态，这使基于 IQP 的量子生成式模型成为早期容错架构上资源高效的量子优势演示的有前景候选。
英文摘要
Quantum generative modelling casts sampling as a generative task: a parametrised quantum circuit is trained such that sampling reproduces a target probability distribution. Instantaneous Quantum Polynomial-time (IQP) circuits combine structural simplicity with complexity-theoretic evidence for quantum advantage. Yet their practical value depends not only on expressivity, but on how efficiently they consume genuinely quantum resources. We study this question through the lens of magic, or non-stabiliserness, as a resource for quantum generative modelling. We show that established fidelity- and geodesic-based notions of computational progress in a projective Hilbert space are ill-suited to generative models, since operational performance is determined by output probability distributions rather than quantum states themselves. We evaluate magic-consumption directly on the probability simplex, using changes in Jensen-Shannon divergence to quantify progress. Applying this framework to trained random γ-sparse IQP circuits shows signatures of efficient magic use, with the dominant contribution arising from two-qubit gates. As IQP circuits produce remarkably low intermediate magic relative to phase-randomised states with the same sampling distributions, this renders IQP-based quantum generative models as promising candidates for resource-efficient demonstrations of quantum advantage on early fault-tolerant architectures.
Comments4 pages, 4 figures
