C076 - Applying a single round of drive (A) to a state prepared in |Psi^+> excites one ion to D5...
Verdict: partial
Location: Supp. Mat. S5
Type / expected artifact: math / math
Claim: Applying a single round of drive (A) to a state prepared in |Psi^+> excites one ion to D5/2 with probability p/2, providing one of the bit-flip-probability estimators.
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:157 (Supp. Mat. S5).
Conclusion
p is an error process (ideal U_A gives no single-ion excitation). Counting: |dd> has 2 susceptible |down> ions -> p~=2r; |Psi+> has 1 |down> ion per branch (|up> spectator of A) -> P(one in e|Psi+)=r=p/2 to leading order. Exact in small-error limit; O(r^2) correction (e.g. 1% at r=0.01), consistent with paper's note that p/2 underestimates total excitation. Model-based reimplementation -> partial.
Verification details
Derivation excerpt: The ideal drive-(A) propagator at a loop-closing time is $U_A=\exp(i\Phi S_{x,e}^2)$ (C012/C013). At the working point $\Phi=\pi/4$ this gives perfect $|\!\downarrow\downarrow\rangle\to|ee\rangle$ collective transfer (C003) and produces zero single-ion ($D_{5/2}$) excitation - the ideal MS drive never leaves exactly one ion in $|e\rangle$. (Confirmed in run.py: the ideal $U_A$ gives $P(\text{one ion in }e)=0$ for all $\Phi$ from both $|dd\rangle$ and $|\Psi^+\rangle$.)
Executable rerun: run.py exited 0 in 0.423s; log verification/C076/attempts/R002/run.log.
Output excerpt:
r p=P(one in e|dd) P(one in e|Psi+) p/2 diff
0.0001 0.00019998 0.00010000 0.00009999 +1.00e-08
0.0010 0.00199800 0.00100000 0.00099900 +1.00e-06
0.0100 0.01980000 0.01000000 0.00990000 +1.00e-04
0.0500 0.09500000 0.05000000 0.04750000 +2.50e-03
0.1000 0.18000000 0.10000000 0.09000000 +1.00e-02
0.2000 0.32000000 0.20000000 0.16000000 +4.00e-02
Leading-order (r<<1): p = 2r(1-r) ~= 2r ; p/2 ~= r = P(one in e|Psi+).
max relative error of p(Psi+)=p/2 over r in [0,0.05] = 5.000e-02
(= r itself, the O(r^2) double-excitation correction, negligible for the