Vincent Steffan

In this paper, we also for the first time properly understand tile codes from a mathematical perspective: While the first paper introducing tile codes gave an ad hoc construction, we rigorously explain how tile codes can be understood through the lens of homological algebra and algebraic geometry.

19.11.2025 13:41 — 👍 1    🔁 0    💬 0    📌 0

Derived automorphisms are a more general concepts that is useful for CSS codes that have certain symmetries but don't allow for automorphisms (stabilizer preserving permutations of qubits and checks). For example, tile codes don't have automorphisms, but always allow for derived automorphisms.

19.11.2025 13:41 — 👍 1    🔁 0    💬 1    📌 0

We call these logical gates "derived automorphisms". We understand the action of these derived automorphisms by constructing a canonical symplectic basis of logical operators supported along lattice boundaries for tile codes, which can be constructed by hand by a simple cellular automaton.

19.11.2025 13:41 — 👍 0    🔁 0    💬 1    📌 0

In our new paper, we propose a fault-tolerant protocol applying parallel logical CNOT gates to a tile code by sliding it. Our new protocol is advantageous for implementation, as it does not require additional connectivity needed for syndrome measurement. It also has very low physical qubit overhead.

19.11.2025 13:41 — 👍 0    🔁 0    💬 1    📌 0

Planar Fault-Tolerant Quantum Computation with Low Overhead Fault-tolerant quantum computation critically depends on architectures uniting high encoding rates with physical implementability. Quantum low-density parity-check (qLDPC) codes, including bivariate b...

In the mean time, Yingli Yang et al. have figured out how one can use lattice surgery-style methods to implement logical gates on tile codes: arxiv.org/abs/2506.18061 The cool thing here is that their protocol does not require any additional connectivity compared to using tile codes as a memory!

19.11.2025 13:41 — 👍 0    🔁 0    💬 1    📌 0

Tile codes (journals.aps.org/prl/abstract...) generalize surface codes by allowing for slightly higher non-locality and connectivity. In return, these codes give more than an order of magnitude savings in terms of physical qubit overhead per logical qubit at some fixed distance.

19.11.2025 13:41 — 👍 0    🔁 0    💬 1    📌 0

🎉🎉 Happy to share our new paper on logical operators and derived automorphisms for tile codes: scirate.com/arxiv/2511.1... 🎉🎉

19.11.2025 13:41 — 👍 15    🔁 2    💬 1    📌 1

New QEC paper out 🙂 Our tile codes are a new and simple approach to construct local codes on a 2D planar lattice. Read more here if you're interested: scirate.com/arxiv/2504.0...

15.04.2025 09:55 — 👍 22    🔁 3    💬 0    📌 1