Engineering CSS surgery: compiling any CNOT in any code

Understand

We introduce a framework for implementing logic in CSS quantum error correction codes, building on the surgery methods of Cowtan and Burton [CB24].

• Our approach offers a systematic methodology for designing and analysing surgery protocols.
• At the physical level, we introduce the concept of subcodes, which encapsulate all the necessary data for performing surgery.
• At the logical level, leveraging homological algebra, subcodes enable us to track the logical operations induced by any surgery protocol, regardless of the choice of logical operator basis.