Universal Parity Quantum Computing*

In this talk, I will present a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on the parity encoding [1,2]. The results show that logical CPhase gates and R_Z rotations can be implemented in the parity encoding with single-qubit operations. Together with logical R_X rotations, implemented via nearest-neighbor CNOT gates and an R_X  rotation, these form a universal gate set. As the CPhase gate requires only single qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms. I will demonstrate the applicability of the 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. I will further propose simple implementations of multi-qubit gates in tailored encodings and an efficient strategy to prepare graph states.

[1] Universal Parity Quantum Computing, Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner, accepted in PRL, preprint arxiv:2205.09505 (2022).

[2] Applications of Universal Parity Quantum Computation, Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner, accepted in PRA, preprint arXiv:2205.09517 (2022).