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.
*This research was supported in part by the NSF Division of Physics via
Grants No. 1416578 and 1820939.
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Presenters
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Leonid Pryadko
- Department of Physics & Astronomy, University of California, Riverside
- University of California, Riverside