Implementation plan: de-chronologize the exposed-reduced-states post
Target file: exposed-reduced-states.qmd (641 lines at plan time).
Problem
The post presents its experiments in the order they were run: one main sweep, then a section titled “What four follow-up experiments settled”. The framing fails on its own terms. It claims four follow-up questions, contains five experimental subsections, and draws on seven result artifacts. A reader who wants to know what was tested must reconstruct it from a narrative of discovery.
The post is a draft toward a scientific paper. It should state the design once and report what each varied factor produced.
Decisions and rationale
Settled through a grilling session. Recorded here because the code and the prose cannot express why the shape was chosen.
Organize by factor, not by claim or by chronology. Every experiment shares one circuit family, one state generator, one start generator, and one pairwise trace-distance metric. What differs is exactly four things: loss function, epoch budget, exposed width, measurement class. Writing the design as a factor table makes “follow-up” inexpressible rather than merely discouraged.
The loss function is one factor with four levels, not two experiments. The objective-comparison artifact has a config identical to the main sweep and declares shared_with_target_sweep: ["reduced_state", "expectation"]. The two overlapping levels reproduce the sweep exactly. Two current sections merge.
Budget is a swept factor, not a correction. Four of five states meet the 0.01 threshold at 4,000 epochs; five of five at 40,000. Nothing was disproved. An optimizer budget was varied and the outcome moved with it. Framed as a factor, no narrative is needed and no information is lost. The rejected alternative was to report only the 40,000-epoch outcome, which would have discarded a real result about this optimizer.
Validation is not results. The exact-gradient check, the downstream data-processing check, and the Hilbert-Schmidt-against-trace ranking check establish that the apparatus works. None reports a finding. Filing them under Results dilutes the four factors that do. They close the design section.
The 200-draw internal-unitary experiment stays in section 2. It answers why the design discards two qubits at all. That is design justification for the criterion, not a measurement of training, and it belongs where the reader meets the question.
Preregistration is a property of the design, not an event. A threshold chosen after seeing data is worthless, so the fact that both were fixed in advance is load-bearing and cannot be cut. It is stated once, as a clause, and the thresholds are then simply compared against. The current text reminds the reader five separate times that the thresholds came first.
Canonical terms: “generated state” and “generated value”. The post named one concept six ways. “generated state” was already the plurality usage at 12 uses. “target” was rejected despite matching the artifacts, because it imports the machine-learning sense of a label; a reader of the sibling copy in shim hit exactly that confusion. The artifact mismatch is already explained under Reproducibility.
Two uncited artifacts get cited. exposed-state-wide-budget-v1 backs the claim that no run at any width hit the epoch limit. exposed-marginal-comparison-v1 backs the marginal-versus-state distances. Both have check scripts. A claim in the body with no listed artifact is the one thing this post’s reproducibility discipline does not tolerate. reduced-state-substitution-v1 stays uncited because the paragraph citing it is being cut as pure chronology.
Corrected during execution. exposed-marginal-comparison-v1 was also slated for citation, on the belief that it backed the marginal-versus-state distances. It does not. exposed-restricted-measurement-v1, already cited, carries every number the post reports for that factor: 8.95e-8, 0.000343, 0.655, 0.751, 0.108, 0.129 and 0.211. The two artifacts share the runs that converged before 4,000 epochs and diverge only in the sixteen that did not, and their worst-pair maxima coincide because the worst pair converged early in both. The marginal-comparison artifact is therefore a 4,000-epoch replicate whose one unique number, a median ratio of 3.59, the post never reports. Listing an artifact no claim uses is the mirror of the problem being fixed, so only exposed-state-wide-budget-v1 was added.
@fig-experiment-design is narrowed, not redrawn. It is hand-drawn, so a redraw is manual work with a real chance of ending up more cluttered than the factor table it would duplicate. Its 5 x 2 x 6 to 15 pairs to 150 counting is the part readers get wrong, so it earns its place describing the four-qubit sweep specifically.
Related work is promoted to its own section. This takes the post from seven sections back to eight. Accepted: the aim was to stop chronology generating sections, not to hit a count, and interleaving literature with measurements would put citations exactly where a reader wants numbers.
Target structure
| Section | Content |
|---|---|
| 1 | The output of one model as the input of another (unchanged) |
| 2 | The categorical boundary (unchanged; keeps the 200-draw experiment) |
| 3 | Experimental design: shared apparatus, factor table, apparatus checks |
| 4 | Results: loss function, epoch budget, exposed width, measurement class |
| 5 | Discussion (short; restatements removed) |
| 6 | Related work (promoted from a subsection of the old section 6) |
| 7 | Limits |
| 8 | Conclusion: the proved claim, then the measured findings |
Stage 1: Experimental design
Goal: Replace section 3 with a design section stating the shared apparatus, a four-factor table, the acceptance criteria, and the three apparatus checks. Success Criteria: No chronological language. Loss function appears as one factor with four levels. Thresholds stated once with a single preregistration clause. The “earlier experiment” paragraph is gone. @fig-experiment-design caption scoped to the four-qubit sweep. Tests: grep finds no “earlier experiment”, “follow-up”, “first version”. Quarto renders without error. Status: Complete
Stage 2: Results
Goal: Merge old sections 4 and 6 into one Results section with four factor subsections in the order loss, budget, width, measurement class. Success Criteria: Old section 6 no longer exists. One sentence marks the register change from four to six qubits. Every number currently reported is still reported. The four-level loss table appears once. Tests: Every numeric value present in the backup is present in the rewrite. No “follow-up” or “settled” framing survives. Status: Complete
Stage 4: Abstract and Conclusion
Goal: Rewrite the abstract by factor. Rewrite the conclusion as the proved claim followed by the measured findings. Success Criteria: Abstract states claim, four factors, limits, in that order. Conclusion separates what is proved from what is measured. Tests: Abstract contains no “follow-up”. Conclusion has no First/Second/ Third/Fourth enumeration mixing proof with measurement. Status: Complete
Stage 5: Mechanical pass
Goal: Retarget cross-references, raise toc-depth, enforce canonical terms, extend the reproducibility table, verify. Success Criteria: Zero references to @sec-followup. toc-depth: 3. Only “generated state” and “generated value” name those concepts. The reproducibility table lists the two added artifacts. Quarto renders clean. Tests: grep -c "@sec-followup" returns 0. Every @sec- and @tbl- and @fig- reference resolves to an existing label. Every claim-bearing number in the body traces to a listed artifact. Status: Complete
Outcome
All five stages complete. The post renders clean under Quarto 1.9.38.
Verified after execution:
- Zero references to
@sec-followup; no dangling@sec-,@fig-or@tbl-reference remains. - Of 59 numeric literals in the pre-rewrite backup, 57 survive. The two that do not are the overlap figures 0.054 and 1.000 from the cut chronology paragraph.
- No occurrence of “follow-up”, “first version”, “assigned state”, “assigned value”, “state to reproduce” or “outputs to reproduce”.
downstream-contraction.svgwas orphaned by the merge and restored to the apparatus checks in section 3.exposed-reduced-states-sweep.svgremains orphaned; it was orphaned before this work and is out of scope.
Addition after the restructuring pass
exposed-marginal-comparison-v1 is now cited and reported, as a budget control on the measurement-class factor. What it establishes is narrow and stated as such: at 4,000 epochs the marginal runs converge between 103 and 1,160 epochs with none at the limit, while 16 of the 30 state runs are cut off, and the state objective still leaves the trained models closer on all five generated states by a factor of 2.70 to 5.51, median 3.59. So the ordering in ?@tbl-measurement does not depend on the state objective having had sufficient budget.
The worst pair under each objective is identical at both budgets to full stored precision. That is reported as an observation and no mechanism is claimed for it. The worst state-trained pair sits on generated state 0, whose six runs stopped at 1912, 2343, 2351, 2466, 2735 and 4000 epochs, so one of the six did reach the limit and the convenient explanation that the worst pair converged early is not supported by the artifact. Establishing why the maxima coincide would need the pair indices, which the artifact’s summaries do not record.
Check script: checks/wide_sweep_result.py, which declares EXPECTED_SCHEMA = "shim.exposed-marginal-comparison.v1".
Precision pass
A later pass replaced vague comparatives with the quantities behind them. It corrected one factual error and one overstatement.
The error: the width rise was described as “roughly fiftyfold per added qubit”. The measured factors are 51.7 from one to two exposed qubits and 23.4 from two to three, so no single factor describes both steps. The text now gives both.
The overstatement: “that is a suspect, not a result”, about the corner in trace distance explaining early stopping. Nothing in the experiments varied step size or measured gradient error near the optimum, so the text now says the explanation is untested and labels it a conjecture.
Vague terms replaced by their measured content: “worse than” by the factor (6.4 for trace distance, 3.3 for its square); “almost unrelated” and “very different” by the median overlap 0.14; “close to empty” by “carries no content beyond equality of state vectors”; “meaningful” and “expensive” by the parameter counts \(2d-2\) against \(d^2-1\); “asks for much more” by 3, 15 and 63 against 18; “the ordinary thing a quantum computer does” by “applies no entangling gate between output wires”; “almost cannot see” and “adequate in practice” by the data-hiding condition, trace distance approaching 1 while restricted separation approaches 0; “gives out” by the width at which the threshold stops being met.
Checked and left alone: “recovers 0.60 of the trace-distance separation at the median pair and 0.87 at the widest”. The maximum per-pair ratio is 0.8719 and the ratio of the two maxima is also 0.8719, so both readings agree and the sentence is correct either way.
Coverage of the precision pass
The first precision pass was driven by a fixed vocabulary of about forty vague words, and it skipped figure-caption lines. It therefore reported no hits in sections 1, 3 and 6, which means only that those sections contain none of those forty words. A second pass read them.
That second pass found a reproducibility gap rather than a wording problem. Section 3 is titled “Experimental design” and described the stopping rule as “until the loss stops falling”. The convergence threshold (\(10^{-9}\) change between successive epochs), the learning rate (0.35) and the finite-difference step (\(10^{-6}\)) appeared nowhere in the article, although “step size” was mentioned three times. All three are now stated in the shared-apparatus paragraph, with the cost of the gradient, two circuit evaluations per parameter per epoch.
Other corrections in the untouched sections:
- Uniqueness of the partial trace was asserted over all maps. It holds for linear maps, and the text now says so.
- \(I_H\) was defined one sentence after its first use; it is now defined at it.
- “Every sufficiently rich set of measurements defines its own norm” replaced by the condition that makes it true: the family’s elements span the Hermitian operators on the system.
- “Restricting the boundary metric remains the right idea” was a value judgment and is now a statement about what the result does and does not rule out.