Quantum computation and error correction based on continuous variable cluster states* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11834010, 11804001, and 11904160), the Natural Science Foundation of Anhui Province, China (Grant No. 1808085QA11), the Program of Youth Sanjin Scholar, National Key R&D Program of China (Grant No. 2016YFA0301402), and the Fund for Shanxi “1331 Project”

Abstract

Measurement-based quantum computation with continuous variables, which realizes computation by performing measurement and feedforward of measurement results on a large scale Gaussian cluster state, provides a feasible way to implement quantum computation. Quantum error correction is an essential procedure to protect quantum information in quantum computation and quantum communication. In this review, we briefly introduce the progress of measurement-based quantum computation and quantum error correction with continuous variables based on Gaussian cluster states. We also discuss the challenges in the fault-tolerant measurement-based quantum computation with continuous variables.