Thanks to my collaborators at U Sydney and OIST. This project began last year at a workshop in Kyoto where Jun presented her work on Bacon-Shor board games. I asked if you could use the same trick with the heavy-hex code. She came back the next day with a schedule presented on a WhatsApp sticker.

In the other arxiv.org/abs/2604.14299 we run numerical simulations of larger instances of the code. We show how different choices of measurement schedules trade off threshold error rates for logical errors in the X and Z bases.

In one arxiv.org/abs/2604.14296 we implement a distance-5 instance of the code in an experiment using IBM's heron device Pittsburgh. We also show how benchmarking tools such as ACES can produce noise characterisation data that can be used to improve decoder performance.

Two papers out today: a double feature introducing the dynamic compass code
arxiv.org/abs/2604.14296
arxiv.org/abs/2604.14299
We find novel measurement schedule for the heavy-hex code to find a 2D code that has a threshold against circuit noise and is readily implemented on the heavy-hex lattice.

Decoder for the Triangular Color Code by Matching on a M\"obius Strip An efficient matching decoder for the color code with boundaries that corrects high-weight errors is proposed, leading to competitive results of practical relevance.

I wrote many papers on this topic now and each one teaches me something new (One highlight is Kaayva's undergraduate work introducing the Möbius strip decoder doi.org/10.1103/PRXQ...). In our new work I learned matching needs to be combined with other decoding methods for better speed and accuracy.

A matching decoder for bivariate bicycle codes The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these...

A link to Kaavya's work here scirate.com/arxiv/2602.2... and my old work with Dom here journals.aps.org/prresearch/a.... Underlying the idea of matching decoders is that of conservation laws and code symmetries. I wrote a perspective on this idea here ieeexplore.ieee.org/abstract/doc....

Some time ago @domwilliamson.bsky.social and I wrote a paper on decoding fracton codes. This gave us the idea to try to extend MWPM decoding to all codes. We didn't get there yet but work led by @kaavyasahay.bsky.social has made great progress showing a matching decoder for bivariate bicycle codes.

I am watching your conspiracy physics video in December, and you asked for a reminder to cancel your Wall Street journal subscription :-)

Intern 2026: Fault-tolerant quantum algorithms

Our team at IBM is looking for interns! If you are interested in researching fault-tolerant quantum algorithms, please apply here: ibmglobal.avature.net/en_US/career...

The deadline is a soft one but don't wait around either. Send me a message if you have any questions.

Intern 2026: Quantum Computing Theory

Are you a graduate student looking for experience working on the theoretical problems we need to solve to build a quantum computer? We are currently accepting applications for internship positions in the quantum computing theory team at IBM for summer 2026.

ibmglobal.avature.net/en_US/career...

Congratulations!

Color code with a logical control-$S$ gate using transversal $T$ rotations The color code has been invaluable for the development of the theory of fault-tolerant logic gates using transversal rotations. Three-dimensional examples of the color code have shown us how its struc...

To those that may have noticed v1 on arXiv, the published article comes with an expanded discussion on the results as supplemental information. This new material is also included as an appendix on the second version on arXiv arxiv.org/abs/2411.15035. Thanks to the referees for their reviews.

We have 3D color codes with transversal T and CCZ gates, so why not a CS gate as well? Here is one such example to fill that gap. I wonder if it is unique. Unlike color codes with T and CCZ gates, I found I needed to use a new boundary that terminates all string logical operators, but no membranes.

New work just published
journals.aps.org/prl/abstract...
I was sat on this result for a couple of years but as you can see in the acknowledgements sometimes I need to be told three times to get things done (and sometimes I need to be asked more than three times, sorry @kenbrownquantum.bsky.social)

It was great to see you there Ken

Excited to share our first major result from our IARPA Entangled Logical Qubits team!

arxiv.org/abs/2504.07258

@benbrown.bsky.social @universal-soup.bsky.social @evanhockings.bsky.social @georgianixon.bsky.social

Lastly, let me mention that many of our gates start and finish with some planar version of the surface code, so our proposal is compatible with conventional surface code quantum computing schemes. That means we can combine our gates with all of its standard Clifford gates to get a universal gate set

We also find these gates can be scaled to produce arbitrarily good magic states, as we can correct the non-Abelian anyons that are created by errors using a just in time decoder. That is even if our stabilizer measurements are not completely reliable.

Not only that, but our observation showed us how to do a whole laundry list of non Clifford gates in 2D on all kinds of microscopic lattices. In fact we've already run a small instance of one of these gates experimentally arxiv.org/abs/2305.13581.

Universal fault tolerant quantum computation in 2D without getting tied in knots We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilize...

Are you a fan of fault-tolerant non-Clifford gates on the 2D surface code?

Have you been wondering what was really going on in the protocols by Bombín and Brown?

We have a new work for you: arxiv.org/abs/2503.15751

Universal fault tolerant quantum computation in 2D without getting tied in knots We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a path integral framework which provides both a macroscopic picture for different logical gates as well as a way to derive the associated microscopic circuits. We also show an equivalence between our approach and prior proposals where a 2D array of qubits reproduces the action of a transversal gate in a 3D stabilizer code over time, thus, establishing a new connection between 3D codes and 2D non-Abelian topological phases. We prove a threshold theorem for our protocols under local stochastic circuit noise using a just-in-time decoder to correct the non-Abelian code.

Logic gates can often be understood in terms of topological phases, so I often felt it was a shortcoming of my work on a 2D CCZ gate that I did not see the analogous physical picture. So I am pleased to share our work arxiv.org/abs/2503.15751 where we show the gate was a non-Abelian phase all along!

Mitigating errors in logical qubits Communications Physics - Quantum error correction produces an enormous amount of data about the quantum system, including information about whether an uncorrectable error is likely. In this work...

Post selection in QEC is not cheating 🤣, but can be scalable and significantly reduce your resources overheads! Check out our newly published paper in @commsphys.bsky.social rdcu.be/d1LuM, a great collab with Sam Smith and @benbrown.bsky.social @sydneyphysics.bsky.social

Encoding a magic state with beyond break-even fidelity - Nature A scheme to prepare a magic state, an important ingredient for quantum computers, on a superconducting qubit array using error correction is proposed that produces better magic states than those that ...

Our work, led by Riddhi Gupta, was just published in Nature

nature.com/articles/s41...

Thanks to my co-authors for all their hard work.

Thanks. Think I got it. I only got onto bsky a few days ago and I haven't spent long working out how to navigate around it just yet.

Please add me. Also to the superconducting qubit one I think I saw you mention a few days ago.