Standard Zero-Noise Extrapolation (ZNE) in Variational Quantum Eigensolvers (VQE) assumes a single global noise-scaling parameter, failing to exploit the heterogeneous and non-linear noise structure inherent to layered quantum circuits. We introduce a multi-parameter noise geometry framework that independently scales the noise contribution of each ansatz layer via structured unitary folding U~ₗ = Uₗ (Uₗ^† Uₗ) ^ ( (lambdaₗ - 1) /2), mapping the full L-dimensional surface E (lambda₁,. . . , lambdaL). We benchmark three extrapolation strategies — scalar polynomial ZNE, multivariate polynomial regression, and Gaussian Process (GP) regression to the zero-noise limit — across ten molecular systems (H₂, LiH, BeH₂, N₂, H₂O, NH₃, HF, CH₄, CO, CO₂) at a challenging circuit depth of L = 12 layers. Three NISQ noise channels are considered: depolarizing, amplitude damping, and coherent over-rotation. At L = 12, raw Hamiltonian errors under depolarizing noise range from 0. 28 Ha (LiH) to 0. 63 Ha (H₂ amplitude damping), growing roughly 2x compared to the same molecules at L = 6. GP ZNE reduces the mean absolute error by 50–59% over scalar ZNE for incoherent noise channels across all ten molecules, while coherent over-rotation is identified as a pathological case where GP uncertainty overwhelms the signal and scalar ZNE is preferable. Separability analysis reveals that depolarizing noise is near-additively separable across layer pairs (S ~= 0. 93) in a molecule-universal manner, whereas coherent over-rotation generates tighter inter-layer coupling (S ~= 0. 89) that worsens with depth. Layer sensitivity rankings at L = 12 show molecule-specific dominant layers that are no longer trivially the first entangling block, underscoring the importance of per-molecule, depth-resolved mitigation strategies. These findings provide quantitative geometric insight into NISQ noise propagation and demonstrate that richer noise models substantially improve the extrapolation fidelity of VQE in the practically relevant regime of deep circuits.
Kylymdar Omorov (Sun,) studied this question.