Cored product codes for quantum self-correction in three dimensions

Brenden Roberts; Jin Ming Koh; Yi Tan; Norman Y. Yao

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arXiv · 2510.05479

Cored product codes for quantum self-correction in three dimensions

Brenden Roberts·Jin Ming Koh·Yi Tan·Norman Y. Yao

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Abstract

The existence of self-correcting quantum memories in three dimensions is a long-standing open question at the interface between quantum computing and many-body physics. We take the perspective that large contributions to the entropy arising from fine-tuned spatial symmetries, including the assumption of an underlying regular lattice, are responsible for fundamental challenges to realizing self-correction. Accordingly, we introduce a class of disordered quantum codes, which we call "cored product codes". These codes are derived from classical factors via the hypergraph product but undergo a coring procedure which allows them to be embedded in a lower number of spatial dimensions while preserving code properties. As a specific example, we focus on a fractal code based on the aperiodic pinwheel tiling as the classical factor and perform finite temperature numerical simulations on the resulting three-dimensional quantum memory. We provide evidence that, below a critical temperature, the memory lifetime increases with system size for codes up to 60000 qubits.

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Brenden Roberts, Jin Ming Koh, Yi Tan, Norman Y. Yao. 2025-10-07. Cored product codes for quantum self-correction in three dimensions. https://arxiv.org/abs/2510.05479

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