Higher-dimensional quantum hypergraph-product codes
ORAL
Abstract
We describe a family of quantum error-correcting codes which
generalize both the quantum hypergraph-product (QHP) codes by Tillich
and Zémor, and all families of toric codes on m-dimensional hypercubic
lattices. Similar to the former, our codes can have finite rates and
power-law distance scaling with bounded-weight stabilizer generators.
Similar to the toric codes, our codes form m-complexes Km, with m≥2. These
are defined recursively, with Km obtained as a tensor product of a
complex Km−1 with a 1-complex parameterized by a binary
matrix. Parameters of the constructed codes are given explicitly in
terms of those of binary codes associated with the matrices used in
the construction.
generalize both the quantum hypergraph-product (QHP) codes by Tillich
and Zémor, and all families of toric codes on m-dimensional hypercubic
lattices. Similar to the former, our codes can have finite rates and
power-law distance scaling with bounded-weight stabilizer generators.
Similar to the toric codes, our codes form m-complexes Km, with m≥2. These
are defined recursively, with Km obtained as a tensor product of a
complex Km−1 with a 1-complex parameterized by a binary
matrix. Parameters of the constructed codes are given explicitly in
terms of those of binary codes associated with the matrices used in
the construction.
–
Presenters
-
Leonid Pryadko
Department of Physics & Astronomy, University of California, Riverside, University of California, Riverside
Authors
-
Weilei Zeng
University of California, Riverside
-
Leonid Pryadko
Department of Physics & Astronomy, University of California, Riverside, University of California, Riverside