Variational Circuit Compiler for Quantum Error Correction

Quantum error correction is vital for implementing universal quantum computing. A key component the encoding circuit that maps a product state of physical qubits into encoded multipartite entangled logical state. Known methods are typically not ``optimal'' either in terms depth (and therefore burden) or specifics target platform, i.e., native gates and topology system. This work introduces variational compiler efficiently finding general error-correcting codes with given hardware. Focusing on noisy intermediate-scale regime, we show how to systematically compile following an optimizing process seeking minimize number operations allowed by hardware obtain highest fidelity gates. We demonstrate our method deriving efficient encoders logic states five-qubit code seven-qubit Steane code. describe ways augment discovered circuits detection. Our applicable quite generally compiling codes.