Quantum pixel representations and compression for N-dimensional images.
The main results reproduced: recomputed values matched the published ones within tolerance.
- ✓Same input data as the authors
- ✓Reported values were directly comparable
- ✓No relevant deviation in data/preprocessing
- ✓No authors-side cause for any deviation
- ✓Any deviation was negligible
- 🟡Reported values were not (fully) derivable from the shared data
- 🟡The central claim did not (fully) hold under reproduction
- 🟡Overall, the reproduction showed a material discrepancy
A 0–100 reproducibility-quality score from the per-question grades, shown as a z-score: standard deviations above (+) or below (−) the mean of comparable assessments.
▸Reproduction agent’s raw note
DESCRIBED WELL ENOUGH -> 1:1 reproduction. QPIXL++ (C++/CMake, commit c2a1b1f; core algorithm byte-identical to paper-era v0.1.0/Zenodo) built and run on «our HPC» compute nodes after a one-line portability patch (#include <algorithm> for GCC>=12; no algorithmic effect). The two headline gate-complexity claims reproduce EXACTLY to the gate (MNIST: 1024 Ry/1024 CNOT/11 qubits; ceramic: 65,536/65,536/17 qubits). The Ry-vs-CNOT compression relationship reproduces exactly at every one of 9 compression levels (Ry%==setting, CNOT%<Ry%). The ceramic reconstructions (Fig 6) match the deposited reference PNGs at 42-54 dB PSNR and are visually indistinguishable. The statevector simulation matches the algebraic reconstruction within integer rounding. NOT pixel-verified: the MNIST Fig-5 panels, because the paper/repo deposited only the MNIST input, not its reconstructions (reproduced by running the pipeline + verified lossless@0% + correct degradation instead). No value appears fabricated; every reported number is re-derivable from shipped code+data.
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Assessment versions
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v1 current initial assessment Score 50assessed: 2026-06-19 ⛓ faf2ce46a632
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- Reproduced
- 2026-06-25
- Rubric version
- v1.0
- Assessed by
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🤖 AI curator · claude (ai-curator room) · v1.0 · run #1 2026-06-19no human curator yet
- Last updated
- 2026-08-05
Provisional, curator- or AI-assessed, and independently checkable. A reproduction outcome states what one attempt could reproduce — not a judgement of the authors.
Deep full-text extraction
Model: sonnetThe paper tests whether quantum image representations (FRQI, NEQR, MCRQI, NCQI and their variants) can be unified under a single general framework (QPIXL) and prepared with substantially fewer quantum gates and no ancilla qubits than prior circuit constructions, while also being compressible without significant loss of image quality.
- ★ QPIXL is a uniform framework that overarches (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI representations resource
- ★ The QPIXL synthesis method reduces gate complexity for all considered quantum pixel representations without introducing ancilla qubits method
- ★ QPIXL circuits scale linearly (O(N)) in the number of pixels and use only Ry and CNOT gates, making them practical for NISQ devices finding
- ★ A proposed circuit/image compression algorithm reduces gates needed to prepare an FRQI state by up to 90% without significantly sacrificing image quality finding
- ★ QPIXL reduces FRQI state preparation gate complexity from the original O(N^2) (and Khan's O(64N log2 N) with ancilla qubits) to O(2N)/O(N) with no ancilla qubits finding
- QPIXL reduces IFRQI gate complexity from O(pN log2 N) to O(pN) and removes the need for ancilla qubits finding
- ★ Algorithms are publicly released as QPIXL++, a Quantum Image Pixel Library built on QCLAB++ resource
- ★ Definition 1 formalizes the 'Square QPIXL' quantum state as an equal superposition over position basis states tensored with a color-encoding state mechanism
| Assay | System | Perturbation | Readout | Platform |
|---|---|---|---|---|
| quantum circuit gate-complexity analysis/synthesis | simulated quantum circuits (theoretical, no specific hardware stated) | none | number/type of elementary gates (Ry, CNOT) required to prepare image states | QPIXL++ (built on QCLAB++) |
| image compression and quality evaluation | example scientific images (FRQI-encoded) | compression algorithm applied to reduce circuit gates | percentage reduction in gates vs. resulting image quality | QPIXL++ |
- ▼ FRQI gate complexity reduced from O(N^2) to O(2N) with no ancilla qubits
- ▼ Prior FRQI improvement by Khan achieved O(64N log2 N) but required log2(N)-2 extra ancilla qubits
- ▼ IFRQI gate complexity reduced from O(pN log2 N) to O(pN), removing ancilla qubits
- ▼ Compression algorithm reduces gates needed to prepare FRQI states for example scientific images up to 90%
- fold_change up to 90% gate reduction (compression of FRQI circuit for example scientific images)
- other O(N^2) (original FRQI gate complexity)
- other O(64 N log2 N) (Khan's improved FRQI gate complexity, requires log2(N)-2 ancilla qubits)
- other O(2N) / O(N) (QPIXL FRQI gate complexity, no ancilla qubits)
- other O(pN log2 N) to O(pN) (IFRQI gate complexity before/after QPIXL)
- count n+1 qubits (original FRQI qubit count for N=2^n grayscale pixels)
Statistical methods review
Model: sonnetA neutral, descriptive read of the statistical approach — what was done, and (for shared learning, not as criticism) what could also have been done.
This is a theoretical computer science and quantum computing paper introducing the QPIXL framework for quantum image representation. The evaluation approach is entirely based on analytical complexity analysis (Big-O gate counts) and computational demonstrations of circuit compression on scientific images; no inferential statistical testing is performed. Results are reported as exact gate counts, asymptotic complexity comparisons between methods, and compression percentages (up to 90% gate reduction) measured on example images.
| Test | Applied to | n | Assumptions |
|---|---|---|---|
| Analytical complexity analysis (Big-O gate counting) | Comparison of QPIXL vs. prior FRQI, IFRQI, NEQR, INEQR, MCRQI, NCQI, INCQI circuit implementations | — | na |
| Computational demonstration of compression ratio | Circuit and image compression experiments on scientific images (up to 90% gate reduction stated) | — | not stated |
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Image quality after compression is described qualitatively (e.g., 'without significantly sacrificing image quality') without a formal quantitative metric↳ Could also: Standard image quality metrics such as Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), or Mean Squared Error (MSE) could also be used to quantify reconstruction fidelity at each compression level — Quantitative image quality metrics would allow readers to reproduce threshold choices, compare across image types, and understand the trade-off curve between gate reduction and fidelity more precisely
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Compression performance (up to 90% gate reduction) is demonstrated on example scientific images without reporting variability across images or image types↳ Could also: Reporting compression ratios across a benchmark set of images with summary statistics (mean, range, or percentiles) could also characterize the method's typical and worst-case behaviour — A single reported maximum may reflect a best-case outcome; distributional reporting across varied images would convey how consistently the compression performs
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Complexity comparisons between QPIXL and prior methods are presented as asymptotic Big-O bounds↳ Could also: Empirical runtime or gate-count benchmarks on quantum circuit simulators across a range of image sizes N could also accompany the asymptotic analysis — Asymptotic complexity describes large-N behaviour; empirical benchmarks at practically relevant sizes would show whether the constant-factor improvements dominate in the regime of current NISQ hardware
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No confidence or uncertainty quantification is reported for the compression experiments↳ Could also: If experiments involve any stochastic elements (e.g., random image selection or threshold choices), bootstrap confidence intervals or sensitivity analyses across parameter settings could also be reported — Uncertainty estimates allow readers to judge the robustness of the reported compression gains to choices made during experimental setup
What was reproduced
The exact results taken into scope, with each reported value next to the value our attempt produced.
Scope — pmid-35546151
Paper: Amankwah, Camps, Bethel, Van Beeumen, Perciano (2022). "Quantum pixel representations and compression for N-dimensional images." Sci Rep 12:7712. DOI 10.1038/s41598-022-11024-y. PMCID PMC9095730.
Code: https://github.com/QuantumComputingLab/qpixlpp (QPIXL++, C++/CMake).
- Latest master commit (cloned for reproduction): c2a1b1f53c0105b2e051840c85afae01e45c3449 (2025-10-04).
- Paper-era release tag: v0.1.0 = bdbf53f58109e9d3822f13b724ba5db9c8eb4ad8 (2021-10-08), which is also the Zenodo deposit 10.5281/zenodo.5557893.
- VERIFIED: the core algorithm headers (
include/qpixl/frqi/circuit.hpp,frqi/util.hpp,util.hpp,pgm.hpp) are byte-identical between v0.1.0 and master. The only diff inexamples/compressedFRQI.cppis a one-character OpenQASM syntax fix (qelib1.inc->qelib1.inc";). => building master reproduces the paper-era algorithm faithfully; gate counts are unaffected.
Data: Zenodo 10.5281/zenodo.5557893 is a snapshot ZIP of the v0.1.0 repo (the
code, not a separate data product). The paper's actual figure data ships INSIDE
the repo at examples/NSR_Journal_Data/ (added after v0.1.0, present in master):
mnist{0,30,60,75,90}.png— Fig 5 reconstructions (MNIST "3", compression 0/30/60/75/90 %)Fig5_{0,50,75,90,95,99}.png— ceramic-composite reconstructions (256x256, compression 0/50/75/90/95/99 %)gray.dat,fwht.dat— grayscale vector and its FWHT coefficients (intermediate). Input images:examples/Example4.pgm(28x28, the MNIST digit). The 0%-compression reference is a lossless reconstruction == the original, so the shipped 0% PNGs double as the inputs for the other compression levels.
Pipeline
compressedFRQI <in.pgm> <out> <compression%> [sim]:
- read PGM, zero-pad pixel vector to next power of two N=2^n;
- convert grayscale -> FRQI rotation angles;
- permuted fast Walsh-Hadamard transform; compression sets the smallest-|coeff|
compression%of WHT coefficients to zero; redundant CNOTs removed by parity; - emit OpenQASM 2.0 circuit + a header with gate statistics (nQubits, nGates, nCNOT, nRY, nH, compression setting, CNOT% & Ry% reductions);
- reconstruct the (compressed) image via inverse permutation + inverse FWHT,
write
out.pgm; optionally statevector-simulate with QCLAB++ ->out_sim.pgm.maxgates = 2^(nQubits-1) = N. nH = nQubits-1.
IN SCOPE (pipeline-derived, attempted)
- C1 Gate complexity / Table 1: QPIXL FRQI = O(N): N Ry + N CNOT, 0 ancilla, n+1 qubits. Check uncompressed (0%) counts: MNIST N=1024 -> ~1024 Ry, ~1024 CNOT, 11 qubits; ceramic N=65536 -> nbQubits 17, gate counts ~2^16=65,536 (Fig 6 text).
- C2 Fig 5 (MNIST) reconstructions: run at 0/30/60/75/90 %, compare
out.pgmpixel-for-pixel tomnist{...}.png. - C3 Fig 5 text claim: "reduction in Ry gates is in perfect agreement with the compression ratio, but ... a smaller reduction in CNOT gates." Verify Ry% ≈ set% and CNOT% < Ry% across levels.
- C4 Fig 6 (ceramic) reconstructions: run at 0/50/75/90/95/99 %, compare to
Fig5_{...}.png; check uncompressed gate count = 65,536. - C5 QCLAB++ simulation: statevector-simulate a small case (sim=1), confirm
out_sim.pgmmatches the algebraic reconstructionout.pgm.
OUT OF SCOPE (not attempted; stated)
- Theoretical complexity proofs and the asymptotic comparison to Le et al. O(N^2) / Khan O(N log N): mathematical, not a runnable pipeline (the >95% reduction in Fig 4 vs Le et al. relies on Le et al.'s un-shipped implementation).
- Any hardware/real-QPU execution (none claimed for this paper's core results).
- NEQR and the unrelated 2024/2025 example folders in current master.
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