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Paper 1
Twisted Fiber Bundle Codes over Group Algebras
Chaobin Liu
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2604.01478
- arXiv
- 2604.01478
We introduce a twisted fiber-bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This construction extends the untwisted lifted product code, recovered when all twists are identities. We show that invertible twists (satisfying a flatness condition) give a complex chain-isomorphic to the untwisted one, so the resulting binary CSS codes have the same blocklength \(n\) and encoded dimension \(k\). In contrast, singular chain-compatible twists can lower boundary ranks and increase the number of logical qubits. Examples over \(R=\mathbb F_2[D_3]\) show that the twisted fiber bundle code can outperform the corresponding untwisted lifted-product code in \(k\) while keeping the same \(n\) and, in our examples, the same minimum distance \(d\).
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Lord Kelvin's Second Cloud
Gilles Montambaux
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.16902
- arXiv
- 2603.16902
On April 27, 1900, William Thomson, better known as Lord Kelvin, delivered a visionary speech before the Royal Institution of Great Britain. In it, he presented two unresolved problems which, to him, appeared fundamental and unavoidable at the turn of the 20th century. He compared them to two clouds obscuring our understanding of physics. Dissipating these two clouds would eventually require the development of special relativity and quantum mechanics. This article revisits the second cloud which, contrary to what is often claimed in the literature, did not concern black-body radiation, but rather the specific heat of polyatomic molecules. To clarify this, the article aims to place Kelvin's speech within the historical context of the time and to situate it within the sequence of developments, from Kirchhoff to the first Solvay Conference in 1911, that marked the path of the extraordinary intellectual adventure that led to the birth of quantum mechanics. It will also be shown that Max Planck's initial motivation was not to solve the problem of the so-called "ultraviolet catastrophe."
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