C059 - Full Error-Sensitivity Figure Reproduction
Verdict: partial
Location: Supp. Mat. S3, Fig. simulations; thesis Fig. 9.6 excerpt supplied by user
Type / expected artifact: plot / numerical simulation
Claim: Fig. (simulations): Bell-state error versus optical-qubit-frequency error, motional-frequency error, fractional Rabi-frequency error, and optical-qubit dephasing rate, for an MS gate, a two-loop MS gate, and 80 cycles of the protocol.
Model: gpt-5
Limitations: paper_text_reimplementation_with_motion, truncated_fock_space_NF8, visual_match_only, no_digitized_paper_data, optical_qubit_low_offset_mismatch
Conclusion
R003 now gives a complete four-panel audit, not only the motional-frequency audit, and it identifies the source of the optical-qubit-frequency discrepancy.
The full reproduction uses two 3-level ions coupled to a truncated motional Fock mode (NF=8), the Supp. Mat. S3 / thesis Eq. 9.15 MS Hamiltonian, the paper parameters δ = 2π × 15 kHz, η = 0.028, Ω = δ/(2η), and 80 protocol cycles. Repump B and drive C are applied to the full spin-motion density matrix, so residual spin-motion entanglement is not discarded. The second rectangular pulse uses the correct absolute Hamiltonian time offset, so the φ_m2 = π − δt phase cancels only the ideal δt phase and leaves the expected extra ε_m t phase when a motional-frequency error is present.
That full persistent spin-motion model reproduces the motional-frequency, Rabi-frequency, and Markovian-dephasing conclusions, but it does not reproduce the low-offset optical-qubit-frequency blue curve from the thesis excerpt. At ε_q / 2π = 0.25 kHz, the direct NF=8 diagnostic gives:
| optical-qubit-frequency convention | 80-cycle singlet error |
|---|---|
| persistent spin-motion through all cycles | 3.59e-3 |
| reset motion after each complete two-pulse drive A | 4.62e-5 |
| reset motion after each rectangular pulse | 4.48e-3 |
| phase-only correlated ground-state Z surrogate | 2.17e-5 |
This explains the discrepancy with the user-provided thesis value of about 2e-5: that value is reproduced by the phase-only/correlated-phase model described in the text, and approximately by discarding motion after each complete two-pulse A step, but not by carrying the residual spin-motion state forward. The previous R003 statement that the optical-qubit-frequency panel was reproduced by the full persistent model was therefore too strong. The paper source says the simulation uses Eq. S6, but the plotted low-error optical-qubit curve behaves like the first-order “Bell phase only” explanation at source/supp_content.tex:109, not like the full persistent spin-motion propagation.
The remaining endpoint checks are:
| error panel | endpoint comparison | reproduced conclusion |
|---|---|---|
| optical-qubit frequency, 1.5 kHz | persistent model: protocol 8.76e-2, single MS 1.77e-1, two-loop MS 2.75e-1 |
qualitative suppression, but low-offset curve mismatches |
| motional frequency, 1.5 kHz | protocol 8.13e-2, single MS 5.43e-2, two-loop MS 3.44e-2 |
no benefit at large error; protocol becomes comparable/worse |
| Rabi-frequency error, 10% | protocol 1.51e-4, single MS 2.69e-2, two-loop MS 2.52e-2 |
strong protocol benefit |
| optical dephasing, 1/ms | protocol 4.50e-1, single MS 1.17e-1, two-loop MS 1.56e-1 |
no protocol benefit |
This fixes the earlier R003 omission and preserves the previous non-motional findings: the Rabi-error panel remains a strong match, and the dephasing panel still shows no protocol advantage. The motional-frequency discrepancy is also resolved: the old local-clock model artificially canceled residual displacement, while the corrected absolute-clock model makes the protocol curve rise as in the paper/thesis figure.
The verdict remains partial with a mismatch limitation. Three of the four panel conclusions are reproduced by the full persistent model, while the optical-qubit-frequency panel requires a phase-only/reset-after-A convention that is not stated explicitly enough in the paper text or thesis excerpt.
Evidence
Sandboxed command:
uv run paper-verifier sandbox -- python run.py
Discrepancy diagnostic:
uv run paper-verifier sandbox -- python qfreq_discrepancy.py
Output excerpts:
panel q: Optical-qubit frequency error (kHz)
x= 1.5: MS=0.17708 MS2=0.27513 protocol=0.087635
panel m: Motional frequency error (kHz)
x= 1.5: MS=0.054281 MS2=0.034438 protocol=0.081323
panel O: Rabi-frequency error (%)
x=10.0: MS=0.026944 MS2=0.025161 protocol=0.00015076
panel G: Optical-qubit dephasing rate (1/ms)
x= 1.0: MS=0.11694 MS2=0.15593 protocol=0.44988
checks: {"dephasing_no_benefit_vs_both_ms_at_1_per_ms": true, "motional_no_benefit_vs_two_loop_at_1p5kHz": true, "qubit_frequency_reduced_vs_single_ms_at_1p5kHz": true, "rabi_reduced_vs_both_ms_at_10pct": true}
decision: partial
Discrepancy diagnostic output:
"persistent_spin_motion": 0.0035905920580150408
"reset_motion_after_two_pulse_A": 4.61559880388096e-05
"reset_motion_after_each_rectangular_pulse": 0.004475351401833083
"phase_only_correlated_ground_Z": 2.172240557019034e-05
Diagnostic figure:
