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Dom Williamson

@domwilliamson.bsky.social
542 followers 316 following 72 posts

Topological phases of matter and fault-tolerant quantum computing at The University of Sydney.

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Dom Williamson @domwilliamson.bsky.social · 16/09/2026
Thanks Yugo & @bartlettquantum.bsky.social for the fun collaboration!
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Dom Williamson @domwilliamson.bsky.social · 16/09/2026
Our algorithm works by mapping the simulation onto a Pauli stabilizer computation that can be efficiently executed by your favorite tool, e.g. stim. We apply this to exactly simulate a recently proposed magic state cultivation protocol. arxiv.org/abs/2609.16929
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Dom Williamson @domwilliamson.bsky.social · 16/09/2026
Quantum computers require magic to run useful algorithms. But classically benchmarking fault-tolerant magic operations is intractable. In new work, led by PhD student Yugo Takada, we introduce an efficient classical algorithm to exactly simulate a broad class of fault-tolerant magic operations.
arxiv.org
Exact efficient simulation of noisy logical magic states using Clifford stabilizers
The preparation of high-fidelity logical magic states is a crucial subroutine for universal fault-tolerant quantum computation (FTQC). Predicting the performance of FTQC and developing improved protoc...
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Dom Williamson @domwilliamson.bsky.social · 04/09/2026
Fractons are immobile quasiparticles in topological phases of matter. In new work, led by Juliette Soule, we generalize fractons to spacetime. This leads to new dynamical quantum phases of matter and floquet codes with no stringlike logical faults in space or time. arxiv.org/abs/2609.03703
Fractons hopping in space (left) and spacetime (right)
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Dom Williamson @domwilliamson.bsky.social · 02/09/2026
The key object in the paper is a defect tube “dube” algebra. Sadly, the referees didn’t like my description of forming the algebra as “rolling a dube”. You’ll have to check out v1 to enjoy that.
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Dom Williamson @domwilliamson.bsky.social · 02/09/2026
Fantastic to see this published in Quantum! This remains one of my favorite papers that I have written. It summarizes years of work on symmetry, defects, and topological order in tensor networks.
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mgualt.bsky.social @mgualt.bsky.social · 25/08/2026
A letter to the math community, to appear in the Notices. In response to what I view as irresponsible messaging and unfortunate decisions from some mathematical leaders influencing many in my department. www.math.toronto.edu/mgualt/math-...
math.toronto.edu
Mathematics and the LLM: 2026 – Coordinate Change
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Dom Williamson @domwilliamson.bsky.social · 24/08/2026
By excluding shorter length chain complexes we were able to avoid the infinite complexity of fracton codes and recover a clean classification of what remains. Paper: arxiv.org/abs/2608.20981 Also check out related recent work: arxiv.org/abs/2608.09913
arxiv.org
A Classification of Translation-Invariant Quantum Codes in Any Dimension
Quantum error-correcting codes with two-dimensional translation invariance are known to be equivalent to copies of the two-dimensional toric code. Such a simple classification is not possible for quan...
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Dom Williamson @domwilliamson.bsky.social · 24/08/2026
Until now. In new work led by PhD student Andrew Li we show that codes based on length-D chain complexes with D-dimensional translation invariance are equivalent to copies of higher dimensional toric codes!
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Dom Williamson @domwilliamson.bsky.social · 24/08/2026
Quantum codes in 2D are pretty simple, they are all equivalent to copies of toric code. In higher dimensions things get a bit wild with multiple types of toric code and infinite families of inequivalent fracton codes. There, the classification question looks a bit like a lost cause.
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Benjamin Pope @benjaminpope.bsky.social · 29/07/2026
Two permanent teaching jobs in maths/stats and physics/astronomy in my old department at UQ! uq.wd3.myworkdayjobs.com/en-GB/uqcare...
uq.wd3.myworkdayjobs.com
Lecturer in Mathematics/Quantitative Science
School of Mathematics and Physics 2 x Full Time, permanent positions Diverse, supportive, and family-friendly work environment Base salary will be in the range of $119,462.94 – $141,545.09 + 17% super...
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Clément Canonne @ccanonne.github.io · 29/07/2026
Spent the day at an event mapping out Quantum Physics, Engineering, and Computing research at #USyd. Seeing so many people engaged and eager to collaborate, I feel energized and optimistic: there is a lot of good stuff to be done, and a lot of will to do so!
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Ben Brown @benbrown.bsky.social · 27/07/2026
I am very happy to see our work on non-Clifford gates with 2D non-Abelian topological phases published in PRX journals.aps.org/prx/abstract.... This is definitely among the most exciting projects I have worked on.
journals.aps.org
Universal Fault-Tolerant Quantum Computation in 2D without Getting Tied in Knots
Researchers have designed a way to perform complex logic gates in two-dimensional quantum computers by temporarily moving data into an exotic non-Abelian phase. This method provides a path toward larg...
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
2) At a high level, conventional symmetries should correspond to transversal gates or local unitary circuits, while noninvertible symmetries are more like staircase circuits or adaptive local unitaries (e.g. in 1D arxiv.org/abs/2311.01439)
arxiv.org
Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models
A systematic approach to dualities in symmetric (1+1)d quantum lattice models has recently been proposed in terms of module categories over the symmetry fusion categories. By characterizing the non-tr...
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
Thanks! 1) I really like this comprehensive work on SETs arxiv.org/abs/1410.4540 (the work from my phd I mentioned is this one arxiv.org/abs/1711.07982)
arxiv.org
Symmetry Fractionalization, Defects, and Gauging of Topological Phases
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the...
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
see also this nice work on a similar topic arxiv.org/abs/2605.28794
arxiv.org
Non-invertible symmetry enriched string net topological orders
We propose a definition of a non-invertible symmetry enriched topological order (NI-SETO), and we implement our definition for string net models. We do so in two ways, using full inclusions of unitary...
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
In our new work we propose that after a general condensation in a topological phase the resulting topological order is enriched by a noninvertible symmetry hypergroup. Thanks to Lea, Clement, Ed, and Campbell for the fun collaboration. @universal-soup.bsky.social
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
Curiously, a similar calculation could be done for general condensations that were not related to finite groups. But it was unclear if one could make sense of symmetry-enrichment in the absence of a finite group... Until now. arxiv.org/abs/2605.28688
arxiv.org
Topological lattice gauge theory enriched by non-invertible symmetry
We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible s...
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Dom Williamson @domwilliamson.bsky.social · 28/05/2026
Towards the end of my PhD, quite a while ago, I was working on extracting the symmetry-enriched topological order that occurs when the gauge charges of a finite group are condensed in a topological phase of matter.
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Dom Williamson @domwilliamson.bsky.social · 20/05/2026
Excited to share our new work led by fantastic undergraduate research student Cassie Hopkin. We show that many translation invariant qLDPC codes can be viewed as compactifications of a single parent fracton code that is local in a higher dimension. arxiv.org/abs/2605.19298 @vva.bsky.social
arxiv.org
Translation-invariant quantum low-density parity-check codes from compactified fracton models
Quantum error-correcting codes with translation symmetry and local checks have been studied extensively, leading to a wide variety of fracton codes in three or more dimensions which lack a complete un...
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Dom Williamson @domwilliamson.bsky.social · 19/05/2026
Very excited to explore new roads to fault-tolerant photonic quantum computation with PsiQuantum! rms.arc.gov.au/RMS/Report/D... @arc-gov-au.bsky.social @sydney.edu.au @psiquantum.bsky.social @bartlettquantum.bsky.social @acdoherty.bsky.social @jcbridgeman1.bsky.social @quantum-roberts.bsky.social
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Aravind (Sri AravindaKrishnan Thyagarajan) @aravind16coiner.bsky.social · 27/04/2026
📢 📢 📢 🚨 I am looking for two PhD students to hire in post quantum cryptography. Exciting opportunity to work at University of Sydney @sydneycompsci.bsky.social and the theory/crypto groups here. Do share with your students and contacts. #hiring #phd #pqc #cryptography 🔗 iacr.org/jobs/item/4199
iacr.org
Two PhD Positions in Post-Quantum Cryptography (PQC)
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Quantum Journal @quantum-journal.bsky.social · 25/04/2026
Freshly published in Quantum: Wire Codes by Nouédyn Baspin and Dominic Williamson doi.org/10.22331/q-2...
quantum-journal.org
Wire Codes
Nouédyn Baspin and Dominic Williamson, Quantum 10, 2083 (2026). Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently,...
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Clément Canonne @ccanonne.github.io · 21/04/2026
The ARC Centre of Excellence in #Mathematics for #Quantum Era Security and Trust (MathQuEST) is hiring a Chief Operating Officer! 3+ years, based in #Sydney. Or, more succinctly: "we're planning a COO!" Details: usyd.wd105.myworkdayjobs.com/en-GB/USYD_E... More about #MathQuEST: mathquest.edu.au
usyd.wd105.myworkdayjobs.com
Chief Operating Officer - MathQuEST
Full time (applicants seeking part-time employment considered), fixed term, initially for 3 years, with possibility of further extension. Located at Camperdown Campus Senior leadership role supporting...
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Clément Canonne @ccanonne.github.io · 15/03/2026
It's official! The Theory of #Quantum Computation, Communication and Cryptography conference (TQC) 2028 will be held in Sydney, 🇦🇺 Australia, in August'28! tqc-conference.org/2026/2027/ #TQC2028 (TQC 2027 will take place in Grenoble, France)
media.tenor.com
a white cockatoo with a yellow beak is standing on a brown surface
Alt: a sulphur-crested cockatoo, looking very happy, showing its head
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Dom Williamson @domwilliamson.bsky.social · 06/03/2026
Rounding out the hat-trick, a new quantum weight reduction procedure that replaces the qubits and checks of an arbitrary quantum code with patches of surface code which are glued following the connectivity of the original code. arxiv.org/abs/2603.04883 Thanks to my collaborators Andrew & Nouédyn.
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Dom Williamson @domwilliamson.bsky.social · 06/03/2026
New work out today on quantum magic state cultivation with flagged low-depth adaptive circuits that gauge logical Clifford operators. arxiv.org/abs/2603.05429 Thanks Bence and Ben for the fun collaboration.
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Dom Williamson @domwilliamson.bsky.social · 06/03/2026
Here’s an artist’s (Andrew’s) depiction of the parsimonious cone (bottom) vs the old unparsimonious construction (top).
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Ben Brown @benbrown.bsky.social · 28/02/2026
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.
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acowtan.bsky.social @acowtan.bsky.social · 19/02/2026
Gave a talk recently at Coogee on constructing and analysing spacetime volumes of LDPC codes & surgeries thereof. Thanks to @sunnyhe.bsky.social @domwilliamson.bsky.social and Ted Yoder for the wonderful collaboration. www.youtube.com/watch?v=Lxzw...
youtube.com
Coogee '26 Talks - Alex Cowtan (Xanadu)
YouTube video by Quantum @ Sydney
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Dom Williamson @domwilliamson.bsky.social · 02/02/2026
New work out today with a killer app for our recent fast and fault tolerant logical measurement procedure on quantum codes. Here we apply it to higher-form Clifford gates to prepare many logical magic states in parallel in constant time. arxiv.org/abs/2601.22939
arxiv.org
Fast magic state preparation by gauging higher-form transversal gates in parallel
Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error...
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Dom Williamson @domwilliamson.bsky.social · 14/11/2025
I had a great time hosting TOPO2025 this week in Sydney. thanks to all the speakers and our sponsors: sites.google.com/view/topowor...
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Tara Murphy @taramurphy.bsky.social · 10/11/2025
We are offering 4 PhD scholarships in #physics and #astronomy topics @sydney.edu.au Including: * FRBs with @manishacaleb.bsky.social * Quantum critical points with @domwilliamson.bsky.social * Nanostructured materials with @boriskuhlmey.bsky.social www.sydney.edu.au/scholarships... ⚛️ 🔭 ☄️ 🧪
sydney.edu.au
Physics Foundation Scholarship
A stipend scholarship to support PhD students who are undertaking research within School of Physics, Faculty of Science at the University of Sydney.
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Sydney Mathematical Research Institute (SMRI) @sydmathinst.bsky.social · 07/11/2025
Come and join us: we have 2x Postdoctoral Research Associate positions available at SMRI. Mathematicians of all areas are encouraged to apply (pure, applied, statistics). Please share with your network #MathSky Closing December 3 usyd.wd105.myworkdayjobs.com/en-GB/USYD_E...
usyd.wd105.myworkdayjobs.com
SMRI Postdoctoral Research Associate
Two (2) Full time, 3 years fixed term opportunities. Located at the Sydney Mathematical Research Institute (SMRI) Opportunity to contribute to research focused on pure or applied mathematics or statis...
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Some cool related works scirate.com/arxiv/2410.1... scirate.com/arxiv/2510.0... scirate.com/arxiv/2510.0...
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Thanks again to the quantum surgeons, Alex, Sunny, and Ted!
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Finally, we introduce a general upper bound on the fault tolerance of any logical measurement scheme in terms of the spacetime region of the code that is addressed by the measurement procedure. Our results point to a tradeoff between overhead and addressability for fault-tolerant quantum logic.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
We demonstrate an equivalence between block reading and homomorphic measurement, and characterize when this equivalence can preserve fault tolerance.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
In the extreme limit of measuring a single logical operator, this scheme reduces to regular lattice surgery with a time overhead that scales with the code distance.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
We go on to study partial block reading We characterize the space and time overhead depending on the properties of the subcode being measured.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Here is what block reading looks like on a pair of surface codes.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Block reading is a simple class of hypergraph surgeries that measure transversal logical operators. These measure logicals across copies of a code block in parallel, in constant time and linear qubit overhead. This doesn’t require the code to be single-shot, similar to algorithmic fault tolerance.
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Dom Williamson @domwilliamson.bsky.social · 17/10/2025
Fault-tolerant logical measurement just got a lot faster! In new work, we show that code surgeries based on hypergraphs, rather than graphs, allow fast and parallel fault-tolerant logical measurements with low qubit overhead (without requiring the code to be single-shot). arxiv.org/abs/2510.14895
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Dom Williamson @domwilliamson.bsky.social · 15/10/2025
This was also fun to listen to.
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Dom Williamson @domwilliamson.bsky.social · 15/10/2025
Quantum low density parity check!
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Dom Williamson @domwilliamson.bsky.social · 14/10/2025
That was fun.
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Dom Williamson @domwilliamson.bsky.social · 14/10/2025
Very happy that I was scheduled to present first today. Talk about a hard act to follow…
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Dom Williamson @domwilliamson.bsky.social · 13/10/2025
Also see related work with similar results plus a bunch of other cool stuff about random input Layer Codes arxiv.org/abs/2510.06659
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Dom Williamson @domwilliamson.bsky.social · 13/10/2025
Applying this decoder to a family of Layer Codes reveals a strong form of partial self-correction where a growing number of encoded qubits are protected for an exponentially long time in the linear system size, up to a scale that is exponential in the inverse temperature. & here is the correction:
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Dom Williamson @domwilliamson.bsky.social · 13/10/2025
The concatenated matching decoder involves rounds of minimum-weight perfect-matching on coupled surface code layers, combined with a decoder for an input Quantum Tanner Code.
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