Building fault-tolerance with unreliable quantum circuits

Achieving computational fault-tolerance requires controlling the propagation of errors. To this end, fault-tolerance has been proposed using quantum circuits with regular structures. However, real quantum hardware often has missing qubits, low qubit connectivity, and non-uniform qubit error rates, making practical fault tolerance challenging to achieve. We build on recent methods for achieving fault tolerance despite irregular hardware characteristics and present a semi-automatic co-design method for implementing quantum error-correcting codes from circuits that, independently, would not be fully considered fault-tolerant. We provide numerical evidence demonstrating the practicality and scalability of our approach.