Self-protected quantum simulation and quantum phase estimation in the presence of classical noise

The decoherence phenomenon inevitably exists in quantum computing processes. Consequently, dynamic suppression of decoherence for instance via dynamical decoupling, quantum error correction codes (QECC) etc. is crucial in accurately executing known or to-be-developed quantum algorithms. While this dynamic zero noise strategy well fits into our expectations for the future of quantum computing, given the status quo, we have launched self-protected quantum algorithms for over 15 years based on the opposite living-with-noise strategy. Here we propose self-protected quantum simulations immune to a large class of classical noise. Accordingly, for readout we generalize the conventional quantum phase estimation to its upgraded version in the presence of classical noise.