Logical qubit encoding and quantum error correction (QEC) have been experimentally demonstrated in various physical systems with multiple physical qubits, however, logical operations are challenging due to the necessary nonlocal operations. Alternatively, logical qubits with bosonic-mode-encoding are of particular interest because their QEC protection is hardware efficient, but gate operations on QEC protected logical qubits remain elusive. Here, we experimentally demonstrate full control on a single logical qubit with a binomial bosonic code, including encoding, decoding, repetitive QEC, and high-fidelity (97.0% process fidelity on average) universal quantum gate set on the logical qubit. The protected logical qubit has shown 2.8 times longer lifetime than the uncorrected one. A Ramsey experiment on a protected logical qubit is demonstrated for the first time with two times longer coherence than the unprotected one. Our experiment represents an important step towards fault-tolerant quantum computation based on bosonic encoding.

Quality of Service (QoS) guarantee is an important component of service recommendation. Generally, some QoS values of a service are unknown to its users who has never invoked it before, and therefore the accurate prediction of unknown QoS values is significant for the successful deployment of Web service-based applications. Collaborative filtering is an important method for predicting missing values, and has thus been widely adopted in the prediction of unknown QoS values. However, collaborative filtering originated from the processing of subjective data, such as movie scores. The QoS data of Web services are usually objective, meaning that existing collaborative filtering-based approaches are not always applicable for unknown QoS values. Based on real world Web service QoS data and a number of experiments, in this paper, we determine some important characteristics of objective QoS datasets that have never been found before. We propose a prediction algorithm to realize these characteristics, allowing the unknown QoS values to be predicted accurately. Experimental results show that the proposed algorithm predicts unknown Web service QoS values more accurately than other existing approaches.

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