Universal Parity Quantum Computing

We propose a universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on parity encoding. We show that logical controlled phase gate and Rz rotations can be implemented in parity encoding with single-qubit operations. Together with logical Rx rotations, implemented via nearest-neighbor controlled-NOT gates and an Rx rotation, these form a universal gate set. As the controlled phase gate requires only single-qubit rotations, the proposed scheme has advantages for several cornerstone quantum algorithms, e.g., the quantum Fourier transform. We present a method to switch between different encoding variants via partial on-the-fly encoding and decoding.