5 citations · 6 across the 8 of their papers we have counts for
12 papers
Cups and Gates II: Operads, twists, and addressable intra-code gates
Nikolas P. Breuckmann, Margarita Davydova, Jens Niklas Eberhardt +2
In Part I, we introduced a general framework for constructing logical gates in quantum CSS codes from cohomology invariants, focusing on cup products and their generalizations from…
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…
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…
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…
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…
Pruning qLDPC codes: Towards bivariate bicycle codes with open boundary conditions
Jens Niklas Eberhardt, Francisco Revson F. Pereira, Vincent Steffan
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architec…
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…
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…
Two proofs of a Jantzen Conjecture for Whittaker Modules
Jens Niklas Eberhardt, Anna Romanov
We define a filtration of a standard Whittaker module over a complex semisimple Lie algebra and and establish its fundamental properties. Our filtration specialises to the Jantzen…
An Intersection Matrix for Affine Hyperplane Arrangements
Jens Niklas Eberhardt, Carl Mautner
For a real affine hyperplane arrangement, we define an integer intersection matrix with a natural -deformation related to the intersections of bounded chambers of the arrangemen…
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
Jens Niklas Eberhardt, Vincent Steffan
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qL…