C025 - A bit-flip error with probability p per cycle reduces the singlet fidelity by ~= 5.2 p wh...
Verdict: verified
Location: Theoretical error analysis; Supp. Mat. S2
Type / expected artifact: numeric / math / numeric
Claim: A bit-flip error with probability p per cycle reduces the singlet fidelity by ~= 5.2 p when uncorrelated and ~= 3.2 p when correlated.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5; verdict_chain verified -> verified.
Source location(s): source/main.tex:145 (Theoretical error analysis).
Conclusion
Steady-state singlet error vs p at optimal Phi=pi/4, gamma=0.221pi, theta=0.716pi, error after drive (A), via 8000-cycle power iteration. Uncorrelated = local M_{x,0}=exp(-i(pi/2)X_e (x) I); correlated = U_x(sqrt(2p)); both parametrized so one-cycle one-ion-flip prob = p. Fitted slopes (p<0.01): uncorrelated 5.25/5.11 -> rounds 5.2; correlated 3.18/3.13 -> rounds 3.2. Paper: 5.2p and 3.2p. Match within tolerance; ratio ~1.65 confirms correlated gives lower steady-state error. Verified.
Verification details
Executable rerun: run.py exited 0 in 0.518s; log verification/C025/attempts/R002/run.log.
Output excerpt:
p=0.001: one-ion-flip prob (matched param) uncorr=1.000000e-03 corr=9.993335e-04 (target 1.000000e-03)
p=0.005: one-ion-flip prob (matched param) uncorr=5.000000e-03 corr=4.983356e-03 (target 5.000000e-03)
p err_uncorr err_corr ratio
5.0e-05 2.624963e-04 1.588850e-04 1.652
1.0e-04 5.248329e-04 3.177132e-04 1.652
2.0e-04 1.049028e-03 6.352000e-04 1.651
5.0e-04 2.617798e-03 1.586304e-03 1.650
1.0e-03 5.219766e-03 3.166970e-03 1.648
2.0e-03 1.037678e-02 6.311510e-03 1.644
5.0e-03 2.548233e-02 1.561297e-02 1.632