We present Aṇubuddhi, a multi-agent AI system that designs and simulates quantum optics experiments from natural language prompts without requiring specialized programming knowledge. The system composes optical layouts by arranging components from a three-tier toolbox via semantic retrieval, then validates designs through physics simulation with convergent refinement. The architecture combines intent routing, knowledge-augmented generation, and dual-mode validation (QuTiP and FreeSim). We evaluated 13 experiments spanning fundamental optics (Hong-Ou-Mandel interference, Michelson/Mach-Zehnder interferometry, Bell states, delayed-choice quantum eraser), quantum information protocols (BB84 QKD, Franson interferometry, GHZ states, quantum teleportation, hyperentanglement), and advanced technologies (boson sampling, electromagnetically induced transparency, frequency conversion). The system achieves design-simulation alignment scores of 8--9/10, with simulations faithfully modeling intended physics. A critical finding distinguishes structural correctness from quantitative accuracy: high alignment confirms correct physics architecture, while numerical predictions require expert review. Free-form simulation outperformed constrained frameworks for 11/13 experiments, revealing that quantum optics diversity demands flexible mathematical representations. The system democratizes computational experiment design for research and pedagogy, producing strong initial designs users can iteratively refine through conversation.