# What are the Main Classes of Quantum Error-Correcting Codes?

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, just the different classes and categories out there. Thanks!

Concatenated codes are used in cases where we know a code that has a finite code distance (and hence finite suppression of errors), but we want arbitrarily good error suppression. For a code with one logical qubit made out of $$n$$ physical qubits, we can increase suppression by using $$n^2$$ physical qubits, then using $$n$$ independent instances of the code to make $$n$$ slightly improved logical qubits, and then using those to make another instance of the code. The end result is a single logical qubit, with better suppression than a single instance of the code could realize. This process can then be continued indefinitely.