When is this archive useful?
Use it when comparing sparse interaction graphs for an Ising energy-optimization ansatz, checking Fisher natural-gradient identities in a commuting Gibbs family, or estimating the conditional-rotation cost of a coherent q-sample. It is a Python research archive, not a general-purpose noncommuting QBM library.
The question-oriented reuse guide maps these tasks to code and evidence. The plain-text retrieval map provides direct links to Markdown documents and version-pinned numerical tables.
Weighted sparse-Ising representation-alignment benchmark: compact tables
The prospectively frozen internal confirmation compares 24 separately generated weighted sparse-Ising targets at n=16 using five parameter seeds and 1,440 trajectories. The representations are a native chain, a random target-supported tree, a maximum-absolute-coupling target-supported tree (MAXJ), and the full target graph. This is not an external replication.
Success means expected energy minus exact ground energy, divided by the spectral gap, is at most 0.1. For these unique-ground-state targets it certifies ground-state probability at least 0.9.
| Condition | Chain | Random tree | MAXJ | Full graph |
|---|---|---|---|---|
| Adam, random | 0.83% | 0.83% | 0.83% | 11.67% |
| Adam, target biased | 3.33% | 17.50% | 35.83% | 70.00% |
| Exact-natural oracle, target biased | 29.17% | 57.50% | 80.83% | 100.00% |
Target-biased initialization uses the retained target coefficient vector plus matched Gaussian noise. The exact-natural oracle uses exact moments and line-search evaluations, not a practical sampled-cost implementation. The sparse models each use 31 parameters and 31 logical conditional-angle entries, with a CNOT upper count of 30. Full graphs use 75-159 angle entries under the stored orders, with median 131. These are logical resources, not hardware or fault-tolerant costs.
Download the compact source tables: Aggregate outcomes (CSV), Primary paired effects (CSV), and Logical preparation resources (CSV). The evidence map links protocols, raw trajectories, analysis, and validators.
What the results do and do not establish
MAXJ is a deterministic baseline supported by this finite benchmark. It is not a universally optimal tree selector or a Chow-Liu forward-KL-optimal estimator. No quantum speedup, favorable asymptotic scaling, hardware advantage, or general noncommuting training method is demonstrated. The archive is not a peer-reviewed journal publication.
A coherent q-sample reproduces classical sampling probabilities and diagonal-observable expectations; it is not the mixed Gibbs state. See the preparation definitions and purification accounting.
A separate temperature-dependent tree study uses ten reused n=8 instances. At the certification temperature, cooling-power-optimal trees have worse projected energies than both best hot-optimal and forward-KL-optimal trees on all ten instances. This is developmental evidence against that criterion, not a universal impossibility result. The full generated atlas is not distributed here.
Reproduction note: Packaged-result checks do not rerun the exhaustive computation. The v1.1.0 full temperature-study regeneration recipe has a known cleanup/validation mismatch. Use the packaged summaries for inspection and read the reuse guide before attempting that route.
How to cite this research archive
Lin, R. (2026). Representation Alignment in Commuting Quantum Boltzmann Machines (Version 1.1.0) [Computer software]. GitHub.
@software{lin_2026_qbm_representation_alignment,
author = {Ruge Lin},
title = {Representation Alignment in Commuting Quantum Boltzmann Machines},
year = {2026},
version = {1.1.0},
url = {https://github.com/GoGoKo699/QBM-Representation-Alignment/releases/tag/v1.1.0},
license = {BSD-3-Clause}
}Evidence commit: 1fc02e89f283225b1d3503749b33c62c30d0a550. Name the result file or supporting study when citing a specific finding. For later changes, also identify the commit used. The original primary result remains in v1.0.0. See citation guidance, CITATION.cff, and the BSD 3-Clause license.