Curator's Take
AI Commentary
This article extends the powerful concept of foliated error correction—already a key tool for fault‑tolerant measurement‑based quantum computing—to arbitrary prime‑dimensional qudits, opening a pathway for high‑dimensional platforms such as photonic circuits to reap the same robustness benefits as qubit systems. By showing that graph‑state constructions and threshold values remain comparable to their qubit counterparts, the work demonstrates that moving beyond two‑level systems does not sacrifice error resilience while potentially offering richer encoding density and more efficient gate synthesis. The inclusion of concrete examples like a d‑dimensional toric code and a generalized honeycomb code ties the theory directly to emerging hardware proposals, making it a timely bridge between abstract coding theory and practical quantum photonics. Readers should note that the reported thresholds assume a simplified error model, so further experimental validation will be needed before full deployment.
— Mark Eatherly
Summary
We present a framework for foliating any Pauli-based quantum error-correcting code over prime-dimensional qudits. For any such code, we obtain a qudit graph state that can be measured to perform fault-tolerant measurement-based quantum computing. Such a paradigm is of interest in platforms such as photonics, where measurement-based protocols are natural and high-dimensional states are readily available. We discuss several examples for arbitrary prime dimension $d$, such as the qudit toric code (stabilizer, CSS), the $d$-dimensional perfect $[[5,1,3]]$ code (stabilizer, non-CSS), and a straightforward $d$-dimensional generalization of the CSS honeycomb code (dynamical, CSS). Under a simple error model, we numerically calculate thresholds for the foliated qudit toric code and demonstrate that they are comparable to the non-foliated version.