11 papers
Optimal Decoding with the Worm
Zac Tobias, Nikolas P. Breuckmann, Benedikt Placke
We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of log…
Copy-cup Gates in Tensor Products of Group Algebra Codes
Ryan Tiew, Nikolas P. Breuckmann
We determine conditions on classical group algebra codes so that they have pre-orientation for cup products and copy-cup gates. This defines quantum codes that have constant-depth…
Cups and Gates I: Cohomology invariants and logical quantum operations
Nikolas P. Breuckmann, Margarita Davydova, Jens N. Eberhardt +1
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology in…
Logical Operators and Derived Automorphisms of Tile Codes
Nikolas P. Breuckmann, Shin Ho Choe, Jens Niklas Eberhardt +2
The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well un…
Expansion creates spin-glass order in finite-connectivity models: a rigorous and intuitive approach from the theory of LDPC codes
Benedikt Placke, Grace M. Sommers, Nikolas P. Breuckmann +2
Complex free-energy landscapes with many local minima separated by large barriers are believed to underlie glassy behavior across diverse physical systems. This is the heuristic pi…
Tile Codes: High-Efficiency Quantum Codes on a Lattice with Boundary
Vincent Steffan, Shin Ho Choe, Nikolas P. Breuckmann +2
We introduce tile codes, a simple yet powerful way of constructing quantum codes that are local on a planar 2D-lattice. Tile codes generalize the usual surface code by allowing for…