Nonclassicality of a delayed remote-controlled quantum computing model

Delegated quantum computing is likely to become the primary means for most people to access quantum computers in the future. However, these hardware inevitably operate beyond clients' control, raising concerns about potentially untrusted servers. A fundamental question thus arises -- how can clients verify that the server is genuinely performing quantum computations? Here, we demonstrate that a class of remote-controlled quantum computing (RCQC) models presents the nonclassical behavior verified in a semi-device-independent way. To achieve this, with slight modifications, these models can be described by the prepare-and-measure scenario. By verifying the violations of dimension witnesses, classical causal models can be ruled out, thereby showing nonclassicality of the RCQC model. Remarkably, in the prepare-and-measure scenario, this class of RCQC models happens to exhibit reversed temporal order in quantum information processing. We also explicitly confirm the nonclassical behaviors of a specific 1-U-M RCQC model belonging to this class as an example. This work bridges the fundamental quantum theory with the practical task of quantum computing.