A Design Space Study of Density Matrix Parameterizations for Diffusion-Based Quantum State Tomography
This paper presents a design space study of density matrix parameterizations for diffusion-based quantum state tomography, introducing a geometric framework based on the Jacobian Gram matrix to reveal that isometric conditioning and physical constraint satisfaction are orthogonal criteria where no single parameterization optimizes both, and demonstrating that while better-conditioned parameterizations improve convergence and fidelity without classifier-free guidance, the inclusion of such guidance can reverse performance rankings due to amplified boundary effects.