8 papers
Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid
Boren Gu, Tamas Noszko, Vincent Steffan +4
High-performance quantum low-density parity-check codes promise substantial reductions in the overhead of fault-tolerant quantum computation, but most constructions require long-ra…
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…
The Parabolic K-motivic Hecke Category
Jens Niklas Eberhardt, Arnaud Eteve
We define and study the parabolic K-motivic Hecke category of a (possibly disconnected) Kac-Moody group. Our main result is a combinatorial description via singular K-theory Soerge…
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…
Universal Koszul Duality for Kac-Moody Groups
Jens Niklas Eberhardt, Arnaud Eteve
We prove a monoidal equivalence, called universal Koszul duality, between genuine equivariant K-motives on a Kac-Moody flag variety and constructible monodromic sheaves on its Lang…
Planar quantum low-density parity-check codes with open boundaries
Zijian Liang, Jens Niklas Eberhardt, Yu-An Chen
Although high-threshold and low-overhead quantum low-density parity-check (qLDPC) codes, such as bivariate bicycle (BB) codes, can reduce the physical-qubit cost by an order of mag…