Dom Williamson
@domwilliamson.bsky.social
Topological phases of matter and fault-tolerant quantum computing at The University of Sydney.
I had a great time hosting TOPO2025 this week in Sydney. thanks to all the speakers and our sponsors: sites.google.com/view/topowor...
November 14, 2025 at 12:00 PM
I had a great time hosting TOPO2025 this week in Sydney. thanks to all the speakers and our sponsors: sites.google.com/view/topowor...
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.
October 17, 2025 at 5:36 AM
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.
We go on to study partial block reading We characterize the space and time overhead depending on the properties of the subcode being measured.
October 17, 2025 at 5:36 AM
We go on to study partial block reading We characterize the space and time overhead depending on the properties of the subcode being measured.
Here is what block reading looks like on a pair of surface codes.
October 17, 2025 at 5:36 AM
Here is what block reading looks like on a pair of surface codes.
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
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
October 17, 2025 at 5:36 AM
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
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
This was also fun to listen to.
October 15, 2025 at 12:43 AM
This was also fun to listen to.
Very happy that I was scheduled to present first today. Talk about a hard act to follow…
October 14, 2025 at 4:27 PM
Very happy that I was scheduled to present first today. Talk about a hard act to follow…
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:
& here is the correction:
October 13, 2025 at 1:46 AM
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:
& here is the correction:
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.
October 13, 2025 at 1:46 AM
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.
How do you correct this error in a Layer Code?
In new work arxiv.org/abs/2510.09218 we introduce a concatenated matching decoder and show that Layer Codes assisted by this decoder are partially self-correcting quantum memories at finite temperature!
In new work arxiv.org/abs/2510.09218 we introduce a concatenated matching decoder and show that Layer Codes assisted by this decoder are partially self-correcting quantum memories at finite temperature!
October 13, 2025 at 1:46 AM
How do you correct this error in a Layer Code?
In new work arxiv.org/abs/2510.09218 we introduce a concatenated matching decoder and show that Layer Codes assisted by this decoder are partially self-correcting quantum memories at finite temperature!
In new work arxiv.org/abs/2510.09218 we introduce a concatenated matching decoder and show that Layer Codes assisted by this decoder are partially self-correcting quantum memories at finite temperature!
Floquet codes fit neatly onto the heavy-hex lattice. In new work out today, we show that making full use of all the heavy-hex qubits allows us to fit two floquet codes at once. We also describe transversal gates and low-depth adaptive circuits to switch to the color code.
arxiv.org/abs/2510.05225
arxiv.org/abs/2510.05225
October 8, 2025 at 4:28 AM
Floquet codes fit neatly onto the heavy-hex lattice. In new work out today, we show that making full use of all the heavy-hex qubits allows us to fit two floquet codes at once. We also describe transversal gates and low-depth adaptive circuits to switch to the color code.
arxiv.org/abs/2510.05225
arxiv.org/abs/2510.05225
Join us on a journey through the gauging nexus between topological and fracton phases. In this work we show how to pass through a web of dualities between topological, symmetry-protected, and fractonic phases of quantum matter, and back again.
arxiv.org/abs/2509.19440
arxiv.org/abs/2509.19440
September 25, 2025 at 6:37 AM
Join us on a journey through the gauging nexus between topological and fracton phases. In this work we show how to pass through a web of dualities between topological, symmetry-protected, and fractonic phases of quantum matter, and back again.
arxiv.org/abs/2509.19440
arxiv.org/abs/2509.19440
The spiders and snakes really made it feel like home.
July 6, 2025 at 8:35 AM
The spiders and snakes really made it feel like home.
A few photos of the neighbors there.
July 6, 2025 at 8:35 AM
A few photos of the neighbors there.
Sad news. I had a great time working at IBM Almaden last year. The park that surrounds the campus is amazing.
July 6, 2025 at 8:35 AM
Sad news. I had a great time working at IBM Almaden last year. The park that surrounds the campus is amazing.
We find that gauging the higher-form symmetry implements a general form of p-string condensation and produces cage-net models that support fracton excitations, both on the lattice and in a field theory formulation.
Thanks Pranay, Abhinav, and Nat for the engaging collaboration.
Thanks Pranay, Abhinav, and Nat for the engaging collaboration.
May 21, 2025 at 6:10 AM
We find that gauging the higher-form symmetry implements a general form of p-string condensation and produces cage-net models that support fracton excitations, both on the lattice and in a field theory formulation.
Thanks Pranay, Abhinav, and Nat for the engaging collaboration.
Thanks Pranay, Abhinav, and Nat for the engaging collaboration.
The fault tolerance of our protocols relies crucially on a just-in-time decoder which we apply to correct errors that can produce non-Abelian anyons.
March 21, 2025 at 4:21 AM
The fault tolerance of our protocols relies crucially on a just-in-time decoder which we apply to correct errors that can produce non-Abelian anyons.
We relate the appearance of non-Abelian anyons to a dimension reduction of a 3D topological code with a special choice of boundary conditions.
March 21, 2025 at 4:21 AM
We relate the appearance of non-Abelian anyons to a dimension reduction of a 3D topological code with a special choice of boundary conditions.
Our protocols for logical magic states preparation work by measuring Clifford logicals. This is equivalent to a code deformation known as a gauging logical measurement.
The process to prepare a CZ magic state is shown below.
The process to prepare a CZ magic state is shown below.
March 21, 2025 at 4:21 AM
Our protocols for logical magic states preparation work by measuring Clifford logicals. This is equivalent to a code deformation known as a gauging logical measurement.
The process to prepare a CZ magic state is shown below.
The process to prepare a CZ magic state is shown below.
Our framework uses domain walls between surface codes and a twisted quantum double model, with non-Abelian D4 anyons, to implement non-Clifford gates and to prepare magic states.
The process to implement a CCZ gate is shown below.
The process to implement a CCZ gate is shown below.
March 21, 2025 at 4:21 AM
Our framework uses domain walls between surface codes and a twisted quantum double model, with non-Abelian D4 anyons, to implement non-Clifford gates and to prepare magic states.
The process to implement a CCZ gate is shown below.
The process to implement a CCZ gate is shown below.
We describe how to integrate many EAC blocks into a modular fault-tolerant architecture for a universal quantum computer.
March 14, 2025 at 6:22 AM
We describe how to integrate many EAC blocks into a modular fault-tolerant architecture for a universal quantum computer.
An extractor allows any logical operator in a code block to be measured fault tolerantly with inbuilt fixed connectivity.
March 14, 2025 at 6:22 AM
An extractor allows any logical operator in a code block to be measured fault tolerantly with inbuilt fixed connectivity.
We call these extractor-augmented code blocks EAC blocks*.
To design extractors, we synthesized a number of recent developments on code surgery.
*No relation to the NEAC.
To design extractors, we synthesized a number of recent developments on code surgery.
*No relation to the NEAC.
March 14, 2025 at 6:22 AM
We call these extractor-augmented code blocks EAC blocks*.
To design extractors, we synthesized a number of recent developments on code surgery.
*No relation to the NEAC.
To design extractors, we synthesized a number of recent developments on code surgery.
*No relation to the NEAC.
Code surgery is a way to perform fault-tolerant quantum logic. Last year, there was a flurry of progress on improving general code surgery. In a new work we synthesize a number of approaches, and some new ideas, into an efficient scheme for parallelized code surgery.
arxiv.org/abs/2503.05003
arxiv.org/abs/2503.05003
March 10, 2025 at 3:43 AM
Code surgery is a way to perform fault-tolerant quantum logic. Last year, there was a flurry of progress on improving general code surgery. In a new work we synthesize a number of approaches, and some new ideas, into an efficient scheme for parallelized code surgery.
arxiv.org/abs/2503.05003
arxiv.org/abs/2503.05003