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

We present a fault-tolerant universal quantum computing architecture that combines noise-biased qubits, the parity architecture, and efficient magic state distillation. The parity architecture functions as a classical LDPC code that facilitates flexible and easily parallelisable logical interactions using only local operations within the code. Its layout can be dynamically adapted to algorithmic requirements, allowing scalable error suppression and the realisation of a universal set of fault-tolerant gates. We demonstrate how multi-qubit rotation gates of any angle can be implemented fault-tolerantly and locally using parity qubits, enabling a powerful and efficient gate set. Building on the properties of noise-biased qubits—such as cat qubits—our approach supports parallel multi-qubit interactions while maintaining low physical overhead, relying only on weight-3 and weight-4 stabilisers on a 2D square lattice. In particular, we discuss how parity codes can be used to implement rotations from higher levels of the Clifford hierarchy more efficiently on biased-noise hardware using tailored codes for distillation.