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Paper 1

No More Hooks in the Surface Code: Distance-Preserving Syndrome Extraction for Arbitrary Layouts at Minimum Depth

Yuga Hirai, Shota Ikari, Yosuke Ueno, Yasunari Suzuki

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.01628

arXiv

2603.01628

Hook errors are a major challenge in implementing logical operations with the surface code, because they can reduce the fault distance below the code distance. This motivates syndrome-extraction circuits that suppress hook-error effects for the stabilizer layouts that appear during logical operations. However, the existing methods either increase circuit depth or require simultaneous execution of measurements and CNOT gates, both of which introduce additional overheads and degrade the threshold. We propose the ZX interleaving syndrome extraction, which preserves the full fault distance $d$ for any surface-code layout with regular stabilizer tiles at minimum depth, i.e., four layers of CNOT gates, without requiring additional circuit depth or simultaneous execution of measurements and CNOT gates. The key idea is to interleave the Z and X stabilizer tiles so that hook-error edges in the decoding graph are shortened and effectively eliminated. Numerical simulations under uniform depolarizing noise for memory and lattice-surgery experiments confirm that the proposed method achieves a full fault distance of $d$, whereas the best existing minimum-depth approach achieves $d-1$. Since the full fault distance is achievable for any regular tiling layout of the surface code, the proposed method may serve as an indispensable technique for practical fault-tolerant quantum computation.

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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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