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Reposted by Vincent Steffan

Jens Eisert @jenseisert.bsky.social · 19/06/2026

Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid. scirate.com/arxiv/2606.1...

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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.

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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.

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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.

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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.

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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!

arxiv.org

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...

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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.

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Vincent Steffan @vincent-st.bsky.social · 19/11/2025

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

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Vincent Steffan @vincent-st.bsky.social · 15/04/2025

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...

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