We show explicit examples where up to k/2 Pauli-product measurements can be performed simultaneously, saturating the same upper bound achieved by the surface code.
The result is a single computational block that naturally supports parallel logical operations, i.e. a QGPU.
In this work we address this limitation through a codeโlogic co-design approach. First, we introduce a new family of codes that admits an addressable logical-qubit basis. Second, we develop a code surgery protocol that allows operations on this basis to be executed in parallel. 3/n
quantum computation. A key challenge, however, is that compiling logic is much more difficult than in surface codes: logical operators can overlap, meaning there limited scope for executing operations in parallel. 2/n
๐ข New paper. ๐๐๐๐: ๐๐๐ซ๐๐ฅ๐ฅ๐๐ฅ ๐ฅ๐จ๐ ๐ข๐ ๐ข๐ง ๐ช๐ฎ๐๐ง๐ญ๐ฎ๐ฆ ๐๐๐๐ ๐๐จ๐๐๐ฌ. A great collaboration w/ Boren Gu, Andi Lui, Armanda Quintavalle, Xian Xu, & @jenseisert.bsky.social
๐ญ๐ฅ๐๐ซ; Quantum LDPC codes are an exciting architecture for fault-tolerant ... 1/n
scirate.com/arxiv/2603.0...
detector matrix. @peter-jan.bsky.social's paper on detector models is a great intro to this arxiv.org/abs/2407.13826 At this point you'll have ample background to follow the STIM tutorials on surface code decoding and enough understanding to apply these tools to other QEC codes.
readout, as these are much easier to set up. The PyMatching documentation explains how you can do this for the Toric code pymatching.readthedocs.io/en/stable/to... Once your comfortable with this, it's time to start with more realistic circuit level simulations using STIM where you decode over a
stabiliser codes in terms of binary matrices via the GF2 mapping (this allows you to use classical coding machinery in the analysis of QEC). At this point you can start expereminting with decoding simulations. I would recommend beginning with code capacity simulations, where you assume perfect
I think it's best to learn the basic theory first: how QEC uses entanglement to create redundancy, how you can use stabilisers to nodestructively measure parities, and understand some of the classic codes such as the Shor and Steane codes. From there, it's important to learn how you can represent
Opening slide of my presentation on Quantum Error Correction at Durham Uninversity. Slide features a picture of the Durham student union and Kingsgate bridge, famously designed by legendary North Eastern arcitect Ove Arup and considered to be one of the world's finest examples of brutalist architecture.
A slide from my presentation comparing surface codes to QLDPC codes. Background: surface codes are a leading approach to QEC, favoured for their local connectivity and straightforward ability to scale to arbitrary distance. However, from a coding theory perspective, they are far from optimal codes, owing to the fact that only a single logical qubit is encoded per patch. In practice, it is estimated that ~1000 qubits will be required per logical qubit in a surface code architecture, making them much less efficient than classical LDPC codes (of the type used in 5G and WiFi) where encoding ratios can be as low as 2-to-1. Quantum LDPC are modelled on classical codes, and it is has been shown (through simulation) that they code achieve encoding densities as low as 50-to-1 (some 20x improvement than surface codes). The tradeoff is that QLDPC codes are much less structured than surface codes, requiring long-range interactions between qubits. The QLDPC Tanner graph shown on the slide depicts a naive layout that I usefully refer to as the "spaghetti connectivity".
Language is redundant by design. The town of Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch in Anglesey Wales is probably the best error corrected placename in the world!
Great day back in Durham visiting @durhamqlm.bsky.social to give a seminar on QEC and our recent work at Quantum Software Lab. Also fun to discuss the fault-tolerance of the Welsh towname Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch w/ @ifanghughes.bsky.social @tobifranzen.bsky.social
I wrote a "Zero to Surface Code Guide" a couple of years ago that doesn't require you to transform into Alexei Kitaev. arxiv.org/abs/1907.11157 There is also the legendary surface code review by Austin Fowler arxiv.org/abs/1208.0928 written in 2012 but is still excellent for learning the basics.
Working on LSD was fun! - Our paper on Localized statistics decoding (LSD) for qLDPC codes is now in print.
LSD is a highly parallelizable, reliability-guided inversion decoder that exploits the clustering of errors. Think of it as a parallel version of OSD.
www.nature.com/articles/s41...
A very enjoyable collaboration @timohillmann.bsky.social, @lucasberent.bsky.social, Armanda Quintavalle, Robert Wille, and @jenseisert.bsky.social
parity-check codes. Our LSD algorithm works as a post-processor for standard belief propagation algorithms and, crucially, is designed from the bottom-up with parallism in mind. This makes it a suitable for implementation on specialised hardware (e.g., GPUs, FPGAs, ASICS) for real-time decoding.
๐๐น;๐ฑ๐ฟ; Any quantum error correction (QEC) protocol is only ever as good as its decoder: a classical co-processor tasked with intrepting stabiliser measurements in real-time. In this work, we propose localised statistics decoding (LSD) as a very general decoding algorithm for quantum low-density ...
๐ข Our paper, ๐๐ผ๐ฐ๐ฎ๐น๐ถ๐๐ฒ๐ฑ ๐๐๐ฎ๐๐ถ๐๐๐ถ๐ฐ๐ ๐ฑ๐ฒ๐ฐ๐ผ๐ฑ๐ถ๐ป๐ด ๐ณ๐ผ๐ฟ ๐พ๐๐ฎ๐ป๐๐๐บ ๐น๐ผ๐-๐ฑ๐ฒ๐ป๐๐ถ๐๐ ๐ฝ๐ฎ๐ฟ๐ถ๐๐-๐ฐ๐ต๐ฒ๐ฐ๐ธ ๐ฐ๐ผ๐ฑ๐ฒ๐, is now published in Nature Communications (Nature Portfolio). Great to see it in print!
www.nature.com/articles/s41...
Your wish will be fufilled: this will be in arXiv V2 ๐
Color code decoding with some big claim: arxiv.org/abs/2508.15743
I wish they could try to benchmark this decoder against the experimental color code data from arxiv.org/pdf/2412.14256 zenodo.org/records/1423...
We are releasing experimental data so people can try out their decoding algorithms!
The QEC25 conference hosted by @yaleqi.bsky.social was really excellent, and videos of all talks are available. So much recent progress on quantum error correction!
qec25.yalepages.org
James Mills introducing Logical Accreditation to #QEC2025 at @yaleqi.bsky.social
See our recent preprint here: arxiv.org/abs/2508.05523
Check out the V2 of our qLDPC decoding paper "An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise". The meme summarizes our approach. @qec.codes
Hardware-tailored logical Clifford circuits for stabilizer codes
scirate.com/arxiv/2505.2...
This first first author paper of Eric appeared yesterday, but was not picked up by Scirate. It suggests novel strategies for implementing logical Cliffords of stabilizer codes under hardware constraints.
Hardware-tailored logical Clifford circuits for stabilizer codes
arxiv.org/abs/2505.20261
It is important to identify strategies for implementing Clifford unitaries at the logical level of stabilizer codes in #quantumerrorcorrection, respecting hardware constraints. Here is one such strategy.
๐ฃ New pre-print on the arXiv today on generalisation of surface code lattice surgery to arbitrary CSS codes w/ Clรฉment Poirson and Robert Booth. Congrats to @clemenson7.bsky.social on his first paper! ๐
Thanks you!
The group's research include:
- Investigating new QEC protocols.
- Designing QEC decoding algorithms for specialised hardware.
- Logical gates for fault-tolerant logic.
- Design and implementation of QEC experiments,
- Developing open-source QEC software.
More details soon!
My group will tackle both the theoretical and practical challenges of building fault-tolerant quantum computers.
I'll be advertising postdoctoral research positions soon. Please get in touch if you're interested in joining or collaborating.
A banner showing a photo of Joschka Roffe. The following text is superimposed on the photo: "Joschka Roffe awarded EPSRC Quantum Technology Career Acceleration Fellowship". The University of Edinburgh School of Informatics logo and the UKRI EPSRC logo are also included in the banner.
Happy World Quantum Day! I'm excited to announce that I will be starting a new group dedicated to quantum error correction (QEC) at The University of Edinburgh Quantum Software Lab, funded by an EPSRC Quantum Technology Career Acceleration Fellowship!
๐ฃ New paper: Computing Efficiently in QLDPC Codes w/ @TeamPhotonic! Lots of great stuff here:
- New subsystem codes w/ transversal gates that efficiently compile full Clifford Group.
- Single-shot decoding
- Huge circuit-level logic sims
scirate.com/arxiv/2502.0...
๐จReminder: The deadline to apply for the Quantum Informatics CDT is tomorrow (15th Jan). Apply below ๐
www.quantuminformatics-cdt.ac.uk
