Analysis of heralded higher-fidelity two-qubit entangling gates with self-correction

For the quantum error correction (QEC) and noisy intermediate-scale quantum (NISQ) algorithms to function with high efficiency, the raw fidelity of quantum logic gates on physical qubits needs to satisfy strict requirement. The neutral atom quantum computing equipped with Rydberg blockade gates has made impressive progress recently, which makes it worthwhile to explore its potential in the two-qubit entangling gates, including Controlled-PHASE gate and in particular the CZ gate. Provided the quantum coherence is well preserved, improving the fidelity of Rydberg blockade gates calls for special mechanisms to deal with adverse effects caused by realistic experimental conditions. Here the heralded very-high-fidelity Rydberg blockade Controlled-PHASE gate is designed to address these issues, which contains self-correction and projection as the key steps. This trailblazing method builds upon the previously established buffer-atom-mediated gate framework, with a special form of symmetry under PT transformation playing a crucial role in the process. We further analyze the performance with respect to a few typical sources of imperfections. This procedure can also be regarded as quantum hardware error correction or mitigation. While this paper by itself does not cover every single subtle issue and still contains many over-simplifications, we find it reasonable to anticipate very-high-fidelity two-qubit quantum logic gate operated in the sense of heralded but probabilistic, whose gate error can reduce to the level of 10^-4-10^-6 or even lower with reasonably high possibilities.