Automorphism gadgets in homological product codes

Understand

The homological product is a general-purpose recipe that forges new quantum codes from arbitrary classical or quantum input codes, often providing enhanced error-correcting properties.

• When the input codes are classical linear codes, it is also known as the hypergraph product.
• We investigate structured homological product codes that admit logical operations arising from permutation symmetries in their input codes.
• We present a broad theoretical framework that characterizes the logical operations resulting from these underlying automorphisms.