Applications of Universal Parity Quantum Computation

Abstract

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 as compared to conventional gate-based implementations while keeping the multi-qubit gate counts comparable. We further propose simple implementations of multi-qubit gates in tailored encodings and an efficient strategy to prepare graph states.