C023 - All errors of drive (A) (with |up> spectroscopically decoupled) can be described through...
Verdict: verified
Location: Theoretical error analysis
Type / expected artifact: math / math
Claim: All errors of drive (A) (with |up> spectroscopically decoupled) can be described through 16 elementary error channels {I_e,X_e,Y_e,Z_e}^{tensor 2} acting on the {|down>,|e>}^{tensor 2} subspace.
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:138 (Theoretical error analysis).
Conclusion
{I,X,Y,Z} on the {down,e} qubit form a complete Hilbert-Schmidt-orthogonal operator basis (single-ion Gram = 2I_4; Pauli algebra X^2=Y^2=Z^2=I, XY=iZ all hold). The 16 tensor products {I_e,X_e,Y_e,Z_e}^{otimes2} have rank 16 and Gram = 4I_16, so they span the full 16-dim operator space on {down,e}^{otimes2}. Hence every error restricted to that subspace (|up> decoupled) is a combination of these 16 elementary channels. Clean mathematical fact -> verified.
Verification details
Executable rerun: run.py exited 0 in 0.558s; log verification/C023/attempts/R002/run.log.
Output excerpt:
X@X == I: True
Y@Y == I: True
Z@Z == I: True
X@Y == iZ: True
Y@Z == iX: True
Z@X == iY: True
single-ion Gram (should be 2*I_4):
[[2. 0. 0. 0.]
[0. 2. 0. 0.]
[0. 0. 2. 0.]