We extend the Prometheus framework for unsupervised phase transition discovery from 2D classical systems to 3D classical and quantum many-body systems, addressing scalability in higher dimensions and generalization to quantum fluctuations. For the 3D Ising model ($L \leq 32$), the framework detects the critical temperature within 0.01\% of literature values ($T_c/J = 4.511 \pm 0.005$) and extracts critical exponents with $\geq 70\%$ accuracy ($β= 0.328 \pm 0.015$, $γ= 1.24 \pm 0.06$, $ν= 0.632 \pm 0.025$), correctly identifying the 3D Ising universality class via $χ^2$ comparison ($p = 0.72$) without analytical guidance. For quantum systems, we developed quantum-aware VAE (Q-VAE) architectures using complex-valued wavefunctions and fidelity-based loss. Applied to the transverse field Ising model, we achieve 2\% accuracy in quantum critical point detection ($h_c/J = 1.00 \pm 0.02$) and successfully discover ground state magnetization as the order parameter ($r = 0.97$). Notably, for the disordered transverse field Ising model, we detect exotic infinite-randomness criticality characterized by activated dynamical scaling $\ln ξ\sim |h - h_c|^{-ψ}$, extracting a tunneling exponent $ψ= 0.48 \pm 0.08$ consistent with theoretical predictions ($ψ= 0.5$). This demonstrates that unsupervised learning can identify qualitatively different types of critical behavior, not just locate critical points. Our systematic validation across classical thermal transitions ($T = 0$ to $T > 0$) and quantum phase transitions ($T = 0$, varying $h$) establishes that VAE-based discovery generalizes across fundamentally different physical domains, providing robust tools for exploring phase diagrams where analytical solutions are unavailable.

翻译：我们将用于无监督相变发现的Prometheus框架从二维经典系统扩展到三维经典及量子多体系统，解决了高维可扩展性问题并实现了对量子涨落的泛化。对于三维伊辛模型（$L \leq 32$），该框架检测到的临界温度与文献值误差在0.01%以内（$T_c/J = 4.511 \pm 0.005$），并以$\geq 70\%$的准确率提取了临界指数（$β= 0.328 \pm 0.015$，$γ= 1.24 \pm 0.06$，$ν= 0.632 \pm 0.025$），通过$χ^2$比较（$p = 0.72$）在无需解析指导的情况下正确识别了三维伊辛普适类。针对量子系统，我们开发了基于复数值波函数和保真度损失函数的量子感知变分自编码器架构。应用于横场伊辛模型时，我们在量子临界点检测中实现了2%的精度（$h_c/J = 1.00 \pm 0.02$），并成功发现基态磁化强度可作为序参量（$r = 0.97$）。值得注意的是，对于无序横场伊辛模型，我们检测到以激活动力学标度$\ln ξ\sim |h - h_c|^{-ψ}$为特征的奇异无限随机临界性，提取的隧穿指数$ψ= 0.48 \pm 0.08$与理论预测（$ψ= 0.5$）一致。这表明无监督学习不仅能定位临界点，还能识别性质不同的临界行为类型。我们通过对经典热相变（$T = 0$至$T > 0$）和量子相变（$T = 0$，变化$h$）的系统性验证，证实了基于变分自编码器的发现方法能够泛化到根本不同的物理领域，为探索缺乏解析解的相图提供了稳健的工具。