Transversal non-Clifford gates for quantum LDPC codes on sheaves
TC Lin - arXiv preprint arXiv:2410.14631, 2024 - arxiv.org
A major goal in quantum computing is to build a fault-tolerant quantum computer. One
approach involves quantum low-density parity-check (qLDPC) codes that support …
approach involves quantum low-density parity-check (qLDPC) codes that support …
Quantum fault tolerance with constant-space and logarithmic-time overheads
QT Nguyen, CA Pattison - arXiv preprint arXiv:2411.03632, 2024 - arxiv.org
In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time
auxiliary classical computation, we construct a fault tolerance protocol with constant-space …
auxiliary classical computation, we construct a fault tolerance protocol with constant-space …
[PDF][PDF] Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query Locally Testable Codes and Lifted Codes
UA First, T Kaufman - Proceedings of the 56th Annual ACM Symposium …, 2024 - dl.acm.org
We show that cosystolic expansion of sheaves on posets can be derived from local
expansion conditions of the sheaf and the poset. When the poset at hand is a cell complex …
expansion conditions of the sheaf and the poset. When the poset at hand is a cell complex …
Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes
SJS Tan, L Stambler - arXiv preprint arXiv:2409.02193, 2024 - arxiv.org
Quantum error correction plays a prominent role in the realization of quantum computation,
and quantum low-density parity-check (qLDPC) codes are believed to be practically useful …
and quantum low-density parity-check (qLDPC) codes are believed to be practically useful …
Maximally Extendable Product Codes are Good Coboundary Expanders
G Kalachev, P Panteleev - arXiv preprint arXiv:2501.01411, 2025 - arxiv.org
We investigate the coboundary expansion property of product codes called product
expansion, which plays an important role in the recent constructions of good quantum LDPC …
expansion, which plays an important role in the recent constructions of good quantum LDPC …
A Zero-Knowledge PCP Theorem
We show that for every polynomial q* there exist polynomial-size, constant-query, non-
adaptive PCPs for NP which are perfect zero knowledge against (adaptive) adversaries …
adaptive PCPs for NP which are perfect zero knowledge against (adaptive) adversaries …
Maximally Extendable Sheaf Codes
P Panteleev, G Kalachev - arXiv preprint arXiv:2403.03651, 2024 - arxiv.org
We study sheaf codes, a type of linear codes with a fixed hierarchical collection of local
codes, viewed as a sheaf of vector spaces on a finite topological space we call coded space …
codes, viewed as a sheaf of vector spaces on a finite topological space we call coded space …