Applications of universal parity quantum computation

We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the quantum Fourier transform and quantum addition. Embedding these algorithms in the parity encoding reduces the circuit depth compared to conventional gate-based implementations while keeping the multiqubit gate counts comparable. We further propose simple implementations of multiqubit gates in tailored encodings and an efficient strategy to prepare graph states.