C081 - Setting the spin-qubit detuning beta = J compensates the AC Stark shift (all drives on re...
Verdict: partial
Location: Supp. Mat. S6
Type / expected artifact: math / math / numeric
Claim: Setting the spin-qubit detuning beta = J compensates the AC Stark shift (all drives on resonance) and is numerically verified to optimize R_t.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain partial -> partial.
Limitations: paper_text_only_reimplementation.
Source location(s): source/supp_content.tex:198 (Supp. Mat. S6).
Conclusion
beta scan of the Liouvillian gap at the paper-optimal point (Omega_C=1.95J,kappa=2.58J,gamma=0.29pi): coarse and fine scans both peak at beta/J = 1.000 (R_t=0.114J vs 0.060J at beta=0); two other operating points (incl. Omega_C=6J) also peak at beta/J=1.000. Steady state at beta=J is the singlet (F=1.000000). Confirms beta=J compensates the AC Stark shift and optimizes R_t. Capped at partial: rests on the reimplemented continuous model. paper opt beta/J=1; computed argmax beta/J=1.000.
Verification details
Derivation excerpt: The collective coupling $\hbar J S_{x,e}^2$ shifts the spin-manifold energies (an AC-Stark-like shift) so that drive (C), nominally resonant, is effectively detuned. The free parameter $\beta$ in $\hbar\beta(\ket{\uparrow}\bra{\uparrow}\otimes \mathbf1+\mathbf1\otimes\ket{\uparrow}\bra{\uparrow})$ detunes the qubit and can be used to put all drives back on resonance. The paper states $\beta=J$ achieves this and is numerically optimal.
Executable rerun: run.py exited 0 in 2.598s; log verification/C081/attempts/R002/run.log.
Output excerpt:
steady-state singlet fidelity (beta=J): 1.000000
beta scan at paper-opt point: argmax beta/J = 1.000, R_t = 0.11424 J
R_t at beta=J: 0.11424 J
R_t at beta=0: 0.06000 J
fine scan argmax beta/J = 1.0000
Omega_C=6.0J kappa=3.0J gamma=0.29pi: argmax beta/J=1.000
Omega_C=6.0J kappa=2.0J gamma=0.10pi: argmax beta/J=1.000