Fault-tolerant quantum computing with the parity code and noise-biased qubits

We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain any desired logical connectivity from nearest-neighbor physical interactions. The code layout can be dynamically adjusted to algorithmic requirements on-the-fly. This allows for implementations with any desired code distance with a universal set of fault-tolerant gates. In addition to the previously explored tool-sets for concatenated cat codes, our approach features parallelizable interactions between arbitrary sets of qubits by directly addressing the parity qubits in the code. The proposed scheme enables codes with less physical qubit overhead compared to the repetition code with the same code distances, while requiring only weight-3 and weight-4 stabilizers and nearest-neighbor 2D square-lattice connectivity.