quantum error correction developers

Abstract: We study collective state preparation and channel encoding in fermionic systems under parity superselection and composition governed by the canonical anticommutation relations. For a two-mode Gaussian state $τ$, we obtain the exact entanglement of formation, $E_{\mathrm F}^{\mathrm{phys}}(τ^{\otimes m})=\lceil m/2\rceil\log2$ for every $m\geq1$. Two copies have the same formation value as one, violating additivity and strong superadditivity, while regularization halves the single-copy value. For an associated Gaussian channel, we determine the minimum output entropy and Holevo information at every blocklength and prove nonadditivity of both. Together, these results give exact answers to the fermionic counterparts of the four additivity questions associated with Shor and Hastings. One physical use carries no classical information, whereas two uses transmit one bit perfectly. The unassisted classical and zero-error classical capacities both equal one half bit per mode. A sharp finite-block bound gives a strong converse: the decoding success probability vanishes at every rate above capacity. These optimizations cover all physical pure-state decompositions and channel inputs, with Gaussian ensembles and classical codes attaining the optima. The formation and minimum output entropy formulas hold for every Rényi order $α\in(0,\infty]$. We also determine the unassisted quantum and zero-error quantum capacities, both equal to one half logical qubit per mode, and prove a strong converse: entanglement fidelity vanishes at every rate above capacity. For a noisy Gaussian family, we determine the one- and two-copy formation values and prove strict nonadditivity at full rank. For $τ$, Bell violation under local parity-preserving measurements first appears at three copies.

Abstract: Sipser-Spielman codes and Dijkgraaf-Witten twisted gauge theories are among the most profound ideas in the last few decades in the areas of computer science and mathematical physics respectively. This work unifies them in the same framework using the language of sheaf cohomology, and produces a new framework of twisted sheaf guage theories describing a class of quantum low-density parity-check (qLDPC) codes with non-Abelian $D_4$ topological order. The corresponding twisted qLDPC code can be obtained from gauging a new type of 0-form sub-complex $\mathbb{Z}_2^3$ symmetry from a qLDPC code defined on a sheaf complex, and can be interpreted as a topological defect network of non-Abelain $D_4$ patches glued together with proper gapped interfaces. As an application, one can use this to realize a \textit{magic state fountain} via the gauging measurement of the addressable logical CZ gates as 0-form subcomplex symmetries in a 2D hypergraph-product on a sheaf complex. This includes a scheme of subdividing an arbitrary constant-rate 2D hypergraph-product code with parameter $[[n,Θ(n), Ω(n^{1/2})]]$ into a quantum sheaf code which allows preparation of $Θ(n^{1/2})$ in parallel, equivalent to the recent geometric construction using the code-to-manifold mapping in (arXiv:2601.06736). Moreover, using the recent sheaf complex and algebraic code constructions by Golowich-Tamo-Zhu (arXiv:2609.27801) with parameter $[[n,Θ(n^{1-ε}), Ω(n^{(1-ε)/2})]]$ for arbitrary small $ε$, one can prepare $Θ(n^{1-ε})$ CZ magic states in parallel and hence achieve an almost-constant magic rate.