Root code for the Category Kingdom
Description
Encodes a finite-dimensional logical Hilbert space into a physical Hilbert space associated with a finite category. Codes on modular fusion categories are often associated with a particular topological quantum field theory (TQFT), as the data of such theories is described by such categories.Cousins
- Group-based quantum code— Category quantum codes whose physical spaces are constructed using a finite group as the category are group codes.
- Planar-perfect-tensor code— Several modular fusion categories can be used to define planar-perfect tensors [1].
Member of code lists
Primary Hierarchy
Parents
Category-based quantum code
Children
Modular-qudit codeQubit Fermion Self-complementary qubit Floquet Fermion-into-qubit Twist-defect color Twist-defect surface Fracton stabilizer Color BB Homological Quantum Reed-Muller CDSC Kitaev surface
Category quantum codes whose physical spaces are constructed using the group \(\mathbb{Z}_q\) as the category are modular-qudit codes.
Galois-qudit codeQubit Floquet Fermion Self-complementary qubit Fermion-into-qubit Twist-defect color CDSC Twist-defect surface Color Homological BB Kitaev surface Quantum QR code Quantum Reed-Muller
Category quantum codes whose physical spaces are constructed using the group \(GF(q)\) as the category are Galois-qudit codes.
References
- [1]
- J. Berger and T. J. Osborne, “Perfect tangles”, (2018) arXiv:1804.03199
Page edit log
- Victor V. Albert (2022-01-08) — most recent
Cite as:
“Category-based quantum code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/category_quantum