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Paper 1

Fragmented Topological Excitations in Generalized Hypergraph Product Codes

Meng-Yuan Li, Yue Wu

Year

2026

Journal

arXiv preprint

DOI

arXiv:2601.09850

arXiv

2601.09850

Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the ground states of exactly solvable spin models also motivates the exploration of many-body orders in the stabilizer codes. In this work, we investigate the fracton topological orders in a family of codes obtained by a recently proposed general construction. More specifically, this code family can be regarded as a class of generalized hypergraph product (HGP) codes. We term the corresponding exactly solvable spin models \textit{orthoplex models}, based on the geometry of the stabilizers. In the 3D orthoplex model, we identify a series of intriguing properties within this model family, including non-monotonic ground state degeneracy (GSD) as a function of system size and non-Abelian lattice defects. Most remarkably, in 4D we discover \textit{fragmented topological excitations}: while such excitations manifest as discrete, isolated points in real space, their projections onto lower-dimensional subsystems form connected objects such as loops, revealing the intrinsic topological nature of these excitations. Therefore, fragmented excitations constitute an intriguing intermediate class between point-like and spatially extended topological excitations. In addition, these rich features establish the generalized HGP codes as a versatile and analytically tractable platform for studying the physics of fracton orders.

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Paper 2

To break, or not to break: Symmetries in adaptive quantum simulations, a case study on the Schwinger model

Karunya Shailesh Shirali, Kyle Sherbert, Yanzhu Chen, Adrien Florio, Andreas Weichselbaum, Robert D. Pisarski, Sophia E. Economou

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.03083

arXiv

2510.03083

We investigate the role of symmetries in constructing resource-efficient operator pools for adaptive variational quantum eigensolvers. In particular, we focus on the lattice Schwinger model, a discretized model of $1+1$ dimensional electrodynamics, which we use as a proxy for spin chains with a continuum limit. We present an extensive set of simulations comprising a total of $11$ different operator pools, which all systematically and independently break or preserve a combination of discrete translations, the conservation of charge (magnetization) and the fermionic locality of the excitations. Circuit depths are the primary bottleneck in current quantum hardware, and we find that the most efficient ansätze in the near-term are obtained by pools that $\textit{break}$ translation invariance, conserve charge, and lead to shallow circuits. On the other hand, we anticipate the shot counts to be the limiting factor in future, error-corrected quantum devices; our findings suggest that pools $\textit{preserving}$ translation invariance could be preferable for such platforms.

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