Direct observable regressor for fermionic shadow spectroscopy on H2 / STO-3G.
Predicts time-evolved expectation values of 28 Majorana observables
(\Gamma_\mu(t) = e^{iH(R)t}\Gamma_\mu e^{-iH(R)t}) as a function of bond
length (R) and time (t), with the goal of feeding the resulting signal
matrix into the Chan et al. shadow-spectroscopy post-processing pipeline to
recover energy gaps without expensive quantum-circuit-side time evolution.
50 held-out geometries on the dense (R \in [0.5, 3.0]) Å grid
((\Delta R = 0.01), 251 total). Trained on the remaining 201.
R bin (Å)
n
pearson_mean
pearson_median
range_ratio
MSE
0.65–1.11
11
0.9859
0.9984
0.9893
3.58e-6
1.11–1.56
8
0.9861
0.9980
0.9903
6.19e-6
1.56–2.02
7
0.9918
0.9982
0.9923
7.07e-6
2.02–2.47
12
0.9987
0.9994
0.9988
2.52e-6
2.47–2.93
12
0.9996
0.9997
0.9995
1.42e-6
all
50
0.9931
0.9967
0.9946
3.71e-6
Pearson is per-observable, then averaged across the 28 observables and reported
as mean and median of those 28 values for each held-out R.
Inputs / outputs
Input.(R, t) where R is bond length in Å and t is propagation time
in atomic units ((\hbar/E_h)).
Output. Length-28 vector of expectation values
(\langle\psi_0(R)|\Gamma_\mu(t)|\psi_0(R)\rangle) for the 28 k=1 Majorana
observables on H2/STO-3G's 4 spin-orbital JW encoding. Initial state
(|\psi_0\rangle) is Hartree–Fock with explicit symmetry-breaking
excitations to populate non-trivial gap manifolds.
Valid range. Trained on (R \in [0.5, 3.0]) Å, (t \in [0, 300]) a.u.
Extrapolation outside is unsupported.
Quickstart
python
1from huggingface_hub import snapshot_download
2from inference import MolecularShadowsRegressor
34# token only needed while the repo is private5m = MolecularShadowsRegressor.from_hub(6"aniketdesh/molecular-shadows-h2-v10",7 revision="v10",# pin the architecture version8 token="hf_...",9)1011import numpy as np
12t_grid = np.linspace(0,300,1500)13y = m.predict_trajectory(R=1.4, t_grid=t_grid)# (1500, 28) trajectory at R=1.4 Å
Training data
Bond-length grid: (R \in [0.5, 3.0]) Å, (\Delta R = 0.01) Å (251 points).
R-grid + HF orbital-energy table for inference-time interpolation
eval_results.json
per-R held-out eval metrics (50 geometries)
eval_summary.json
aggregate metrics
history.json
training loss / val MSE curves
README.md
this file
Versioning
v10 (current): HF orbital-energy freq_net + dense R-grid + 6×768 trunk.
Mean Pearson 0.993 across the full PES.
Future versions (v11+) will be pushed as new commits on main with new
tags. Pin via revision="v10" to preserve loading across architecture
changes; main always tracks the latest.
