C052 - Correlated bit/phase flips are modelled by U_i(epsilon) = exp(i (epsilon/2) sigma_{i,down...
Verdict: verified
Location: Supp. Mat. S2
Type / expected artifact: math / math
Claim: Correlated bit/phase flips are modelled by U_i(epsilon) = exp(i (epsilon/2) sigma_{i,down e}) tensor exp(i (epsilon/2) sigma_{i,down e}) (i=x bit-flip, i=z phase-flip), applied once per cycle after drive (A).
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/supp_content.tex:70-74 (Supp. Mat. S2).
Conclusion
U_i(eps)=exp(i(eps/2)sigma_{i,de}) (x) exp(i(eps/2)sigma_{i,de}) is unitary, swap-symmetric, and of identical-factor kron(u,u) form (same single-ion rotation applied coherently to both ions => correlated coherent error). At eps=pi the single-ion factor = iX (x, bit-flip) / iZ (z, phase-flip) on {down,e} and leaves |up> fixed, matching the x=bit-flip / z=phase-flip labelling. Clean mathematical fact -> verified.
Verification details
Executable rerun: run.py exited 0 in 0.525s; log verification/C052/attempts/R002/run.log.
Output excerpt:
i=x: unitary=True swap-symmetric=True kron(u,u) form=True
i=z: unitary=True swap-symmetric=True kron(u,u) form=True
u_x(pi) == i X on {down,e}: True
u_z(pi) == i Z on {down,e}: True
u_x leaves |up> fixed: True
u_z leaves |up> fixed: True
eps=0.05: P(one-ion flip from |dd>) = 1.248959e-03 (approx eps^2/2 = 1.250000e-03)
VERDICT_OK: True