Ben Brown

Ben Brown

@benbrown.bsky.social

Research scientist at IBM Quantum

383 followers78 following31 posts

Ben Brown
@benbrown.bsky.social

Not only does it explain the physical processes behind the 2+1D non Clifford gates I worked on earlier in my career, but it also generalises them. We also connect non-Abelian 2D phases to 3D codes with non-Clifford transversal gates. And we show how to decode these gates under local circuit noise.

Ben Brown
@benbrown.bsky.social

I already thanked my coauthors when I posted about this work when it appeared on the arXiv, but thanks again to them. This ended up turning into something of a monster paper with many different perspectives on the topic.

Ben Brown
@benbrown.bsky.social

This never happened to me before, but this week it happened twice - I got cold two emails asking me for an arXiv endorsement. Anyone else seen this? Is it a scam? I don't see what anyone gets out of it other than an opportunity to spam the arXiv.

Ben Brown
@benbrown.bsky.social

"My concern is mostly about scope and relative impact. The decoder feels quite tied to the BB-code setting.” -An excerpt of the referee report from the QEC workshop for a paper titled "A matching decoder for bivariate bicycle codes"

Ben Brown
@benbrown.bsky.social

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.

Ben Brown
@benbrown.bsky.social

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.

Ben Brown
@benbrown.bsky.social

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.

journals.aps.orgDecoder for the Triangular Color Code by Matching on a M\"obius StripAn efficient matching decoder for the color code with boundaries that corrects high-weight errors is proposed, leading to competitive results of practical relevance.
Ben Brown
@benbrown.bsky.social

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.

Ben Brown
@benbrown.bsky.social

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.

arxiv.orgColor code with a logical control-$S$ gate using transversal $T$ rotationsThe 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...
Ben Brown
@benbrown.bsky.social

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!

arxiv.orgUniversal fault tolerant quantum computation in 2D without getting tied in knotsWe 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.
View full thread
Ben Brown
@benbrown.bsky.social

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.

Ben Brown
@benbrown.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

Ben Brown
@benbrown.bsky.social

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!

arxiv.orgUniversal fault tolerant quantum computation in 2D without getting tied in knotsWe 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.

Ben Brown reposted

Dom Williamson
@domwilliamson.bsky.social

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

arxiv.orgUniversal fault tolerant quantum computation in 2D without getting tied in knotsWe 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...

Ben Brown reposted

Stephen Bartlett
@bartlettquantum.bsky.social

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

rdcu.beMitigating errors in logical qubitsCommunications 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...

You are up to date.