C029 - Motion-including re-verification of the error-sensitivity comparison
Verdict: partial
Location: Theoretical error analysis; Supp. Mat. S3
Type / expected artifact: empirical / math / Fig. simulations.pdf
Claim: Compared to a single MS gate or a two-loop phase-modulated MS gate based on H_A, the protocol reduces the effect of qubit frequency errors and Rabi frequency errors, but offers no benefit for motional frequency errors or fast (Markovian) optical qubit dephasing.
Models: extraction claude-opus-4-8; verification gpt-5; verification_chain claude-opus-4-8 -> gpt-5 -> gpt-5; verdict_chain partial -> partial -> partial.
Limitations: paper_text_reimplementation_with_motion, truncated_fock_space_NF8, coarse_qualitative_grid, optical_qubit_low_offset_mismatch.
Source location(s): source/main.tex:147 and source/supp_content.tex:88-115.
Conclusion
R003 builds the missing motion-including model: two 3-level ions coupled to a truncated motional Fock mode (NF=8), using the Supp. Mat. S3 sideband Hamiltonian, carrying the full spin-motion density matrix through 80 protocol cycles, and applying repump B and drive C without tracing away motion. The second pulse uses the correct Hamiltonian clock offset, so a motional-frequency error leaves the phase-space loop open instead of cancelling by construction.
The reproduced comparisons support three legs of C029 and expose a mismatch in the low-offset optical-qubit-frequency leg:
| error leg | endpoint comparison | result |
|---|---|---|
| optical-qubit frequency error | at 1.5 kHz: protocol 0.0876 vs single MS 0.1771 and two-loop MS 0.2751 | reduced at high endpoint, but low-offset curve mismatches |
| Rabi-frequency error | at 10%: protocol 0.000151 vs single MS 0.0269 and two-loop MS 0.0252 | reduced |
| motional-frequency error | at 1.5 kHz: protocol 0.0813 vs two-loop MS 0.0344 | no benefit vs the phase-modulated MS comparator |
| Markovian optical-qubit dephasing | at 1/ms: protocol 0.4499 vs single MS 0.1169 and two-loop MS 0.1559 | no benefit |
This keeps the claim verdict at partial. The previous spin-only attempts could not test motional-frequency and dephasing legs; the motion-including R003 model fixes that, but the C059 low-offset optical-qubit-frequency diagnostic shows that persistent spin-motion propagation gives 3.59e-3 at 0.25 kHz, not the thesis-scale ~2e-5. The thesis-scale value is recovered only by a phase-only/reset-after-A convention (2.17e-5 to 4.62e-5), so C029 should not be marked fully verified.
Verification details
Executable rerun: run.py exited successfully in the project sandbox and wrote results.json plus motion_c029_diagnostic.png.
Output excerpt:
panel q: Optical-qubit frequency error (kHz)
x= 1.5: MS=0.17708 MS2=0.27513 protocol=0.087635 nbar_protocol=1.551 edge=0.0176
panel m: Motional frequency error (kHz)
x= 1.5: MS=0.054281 MS2=0.034438 protocol=0.081323 nbar_protocol=0.6823 edge=0.00914
panel O: Rabi-frequency error (%)
x=10.0: MS=0.026944 MS2=0.025161 protocol=0.00015076 nbar_protocol=0.0004791 edge=1.9e-06
panel G: Optical-qubit dephasing rate (1/ms)
x= 1.0: MS=0.11694 MS2=0.15593 protocol=0.44988 nbar_protocol=3.067 edge=0.084
checks: {"dephasing_no_benefit_vs_both_ms_at_1_per_ms": true, "motional_no_benefit_vs_two_loop_at_1p5kHz": true, "qubit_frequency_low_offset_matches_thesis_scale_at_0p25kHz": false, "qubit_frequency_reduced_vs_single_ms_at_1p5kHz": true, "rabi_reduced_vs_both_ms_at_10pct": true}
decision: partial
Diagnostic figure:
Modeling notes
The compact printed Eq. S6 is expanded into Hermitian red/blue-sideband terms. At epsilon_q = 0 this is algebraically the same as the compact expression; for epsilon_q != 0 it avoids the unphysical non-Hermitian evolution produced by treating the two unequal sideband frequencies as a single factor multiplying a Hermitian spin operator.
The Fock cutoff is one numerical limitation. At the largest dephasing endpoint the edge population is 0.084, so that point is useful for the qualitative conclusion but not for precision digitization. The more important limitation is interpretive: the optical-qubit-frequency panel is only reproduced if the qubit detuning is reduced to the correlated phase channel described in the text, or if residual motion is discarded after the complete two-pulse A step. The persistent spin-motion model produces a larger low-offset error.
