DCP Challenge: Author Correction and Follow-Up Analysis

This repository accompanies the 2022 article:

Ruge Lin and Weiqiang Wen, “Quantum computation capability verification protocol for noisy intermediate-scale quantum devices with the dihedral coset problem,” Physical Review A 106, 012430 (2022).
DOI: 10.1103/PhysRevA.106.012430 - arXiv: 2202.06984

Scientific status - updated 7 September 2026

The original ParitySolve circuit is correct on its selected collision branch, but the original capability-verification interpretation is not.

The quantity denoted by $p_B$ in the article is the success probability of one specified all-Hadamard decoder. For one original DCP sample, that decoder is in fact optimal even against arbitrary quantum measurements under the stated uniform-secret priors. The failure begins when several samples reuse the same hidden secret: outcomes that reveal no parity individually can become informative through their correlations.

An exact two-sample counterexample uses the same product measurements and only changes the classical decoder:

$$ p_B=\frac{23}{32}, \qquad p_{\rm better}=\frac{25}{32}. $$

Therefore, this repository no longer presents $p>p_B$ as verification of quantum-computation capability.

Retained: the DCP sample construction, the Fourier-label collision mechanism, the selected ParitySolve algebra, and the circuit as a structured hardware-sensitive workload.

Withdrawn: the claim that the published $p_B$ threshold is an adversarially sound capability-verification bound.

The complete statement is available in:

• Current self-contained technical note

• Current technical note in PDF (v1.2.1 release)

• Scientific release review

• September scientific revision and proofs

• Dated August author correction in Markdown

• Dated August correction in PDF

• Scientific status and claim map

This is an author-maintained repository correction by Ruge Lin. It is not an APS Erratum, has not been peer reviewed as a replacement article, and does not alter the journal version.

The proof-of-concept IBM experiment is preserved in the historical code but is outside the scope of the present correction.

Revised scientific conclusions

The September revision adds scientific results, not just numerical implementation changes:

• Global optimality and a limitation on repairing the baseline. The original special-outcome rule is optimal over every one-sample quantum measurement. Independently refreshing the full secret within a fixed parity class makes it globally optimal for any number of samples, so that repair also eliminates the collective accuracy advantage.
• Exact answer-rate frontier. For the ideal pair source, joint confidence can exceed the best separable confidence only when the total conclusive rate is $q<1/N$. Zero-error answers have maximum rate $1/(2N)$. Increasing $N$ does not enlarge the best confidence gap; it lowers the usable answer rate.
• Stronger single-round witness. An exact partial-transpose certificate extends the null to positive-partial-transpose (PPT) measurement effects. An ideal violation requires a negative partial transpose in a conclusive effect. The repeated-round operational theorem still uses separable instruments and separable memory.
• Explicit source-error boundaries. A common, secret-independent local channel preserves the original null. Arbitrary small preparation leakage does not preserve its loss-independent 75 percent confidence ceiling. A conservative calibrated-source allowance and fixed-total-round statistical test are proved, with actual hardware calibration still outstanding.

These are non-peer-reviewed repository results dated 7 September 2026. They are not attributed retroactively to the 2022 article or the August correction. The original shared-secret verification claim remains withdrawn.

Historical record

The repository state that accompanied the article is preserved unchanged at the immutable tag and release:

paper-2022-original

The six original root scripts remain byte-for-byte unchanged:

IBM.py
benchmarking.py
circuit.py
compare.py
proba.py
verification.py

They are retained for historical reproducibility and described in ORIGINAL_2022_CODE.md.

Corrected results at a glance

Figure	$(n,m,t)$	Published $p_B$	Published upper bound	Exact honest probability	Full-likelihood all-H
5(a)	$(4,6,1)$	0.660533	0.664083	0.652965	0.810940, exact
5(b)	$(6,9,4)$	0.716371	0.817392	0.810918	0.937289, Monte Carlo
5(c)	$(9,21,9)$	0.654461	0.906606	0.904804	0.957183, Monte Carlo

The exact honest probability is computed from the complementary-pair occupancy formula in src/dcp_challenge/exact_probabilities.py.

Reproduce the correction

The corrected analysis does not require Qibo.

python -m pip install -e .[test]
python examples/reproduce_counterexample.py
python examples/reproduce_one_sample_optimality.py
python examples/reproduce_figure5.py
python scripts/verify_historical_files.py
python scripts/verify_checksums.py
python scripts/validate_committed_results.py
pytest -q

Expected central output:

Published special-outcome decoder: 23/32 = 0.718750
Same measurements, better decoder: 25/32 = 0.781250

See REPRODUCIBILITY.md for fixed seeds, exact-versus-numerical distinctions, and validation tolerances. The completed checks are summarized in VALIDATION_RECORD.md.

Numerical maintenance - 7 September 2026

The numerical hardening introduced in version 1.1.1 provides stable binomial and log-probability calculations, validation of every committed result field, deliberate-corruption tests, and complete checksum verification. The August scientific correction, PDF, and historical scripts are unchanged. See the reproducibility guide for the distinction between recomputation and archived Monte Carlo checks.

Separate follow-up: phase-twirled heralded DCP witness

The directory witness/ contains a new 2026 follow-up. It is not part of the 2022 article and is not a general proof of quantum computation.

Its narrow ideal-model claim is:

For the ideal source, adaptive separable instruments with separable memory have conclusive error at least $1/4$, while a Bell measurement has zero error and conclusive probability $1/(2N)$. Source errors must satisfy the separately stated noise or calibration assumptions.

This is a DCP-specific maximum-confidence witness of a nonseparable joint measurement. For $N=2$, the complete circuit uses four qubits, at most three CNOT gates, only Clifford operations, and no mid-circuit measurement.

The historical chronology and relation to later work makes the priority boundaries explicit. The 2022 DCP article predates Lee and Bae’s 2026 GLOBAL-versus-SEP maximum-confidence framework as an early trusted-input attempt to test joint inter-cell processing, but it did not prove their sound separation. The sound DCP-specific witness was developed only in the August 2026 reanalysis.

AI-assisted reanalysis

The August 2026 correction and follow-up were developed with substantial assistance from OpenAI’s GPT-5.6 Pro, including literature research, adversarial mathematical checking, numerical validation, code review, and preparation of the reproducible package. Ruge Lin reviewed the resulting claims and accepts responsibility for the repository’s scientific content.

See AI_ASSISTED_REANALYSIS.md for the full methodology and responsibility statement.

Repository map

correction/                  Formal author correction, PDF, TeX, and claim ledger
src/dcp_challenge/           Corrected analytical implementation
examples/                    Small one-command reproductions
tests/                       Exact regression and full-state tests
results/                     Machine-readable committed outputs
witness/                     Separate non-peer-reviewed follow-up construction
AI_ASSISTED_REANALYSIS.md    AI methodology, credit, and responsibility statement
IBM.py ... verification.py   Original 2022 scripts, unchanged

Machine-readable results

• results/correction_core_results.json
• results/one_sample_optimality.json
• results/figure5_corrected.csv
• results/heralded_witness_results.json
• results/validation_crosschecks.json
• results/scientific_revision_results.json

Citation

For the original ParitySolve construction and published article, cite:

@article{lin2022dcpchallenge,
  author  = {Ruge Lin and Weiqiang Wen},
  title   = {Quantum computation capability verification protocol for noisy intermediate-scale quantum devices with the dihedral coset problem},
  journal = {Physical Review A},
  volume  = {106},
  pages   = {012430},
  year    = {2022},
  doi     = {10.1103/PhysRevA.106.012430}
}

When relying on the corrected analysis, also identify:

Ruge Lin, “Author Technical Correction and Updated Analysis” for the DCP challenge article,
DCP-challenge repository, author-correction-2026, 17 August 2026.

For the September optimality, answer-rate, and source-error results, also identify:

Ruge Lin, “Scientific Revision: Global Optimality, Answer-Rate Limits, and Source Errors,”
DCP-challenge repository, version 1.2.0, 7 September 2026.

License status

No software license has been added in this correction. Ordinary copyright restrictions therefore apply unless an explicit license is added later.