Quantum automated learning

Machine learning is widely believed to be a practical application of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies on gradients of model parameters and will become infeasible as quantum learning models scale up. We introduce quantum automated learning, where no variational parameter is involved and the training process is converted to quantum state preparation. In particular, we encode training data into unitaries and iteratively evolve a random initial state under these unitaries and their inverses, with a target-oriented perturbation towards higher prediction accuracy sandwiched in between. Under reasonable assumptions, we prove that the evolution converges exponentially to the desired state corresponding to the global minimum of the loss function. The training process can be understood from the perspective of imaginary time evolution, where the model is trained in an automated fashion. We prove that the quantum automated learning paradigm features universal representation power and good generalization ability with the generalization error upper bounded by the ratio between a logarithmic function of the Hilbert space dimension and the number of training samples. Our results establish an unconventional quantum learning strategy that is gradient-free with provable and explainable trainability, which would be crucial for large-scale practical applications of quantum computing in machine learning scenarios.