Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Quantum Convolutional Neural Networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This provides an analytical guarantee for the trainability of randomly initialized QCNNs, which singles out QCNNs as being trainable unlike many other QNN architectures. To derive our results we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results.

Recurrent machines for likelihood-free inference

Likelihood-free inference is concerned with the estimation of the parameters of a non-differentiable stochastic simulator that best reproduce real observations. In the absence of a likelihood function, most of the existing inference methods optimize the simulator parameters through a handcrafted iterative procedure that tries to make the simulated data more similar to the observations. In this work, we explore whether meta-learning can be used in the likelihood-free context, for learning automatically from data an iterative optimization procedure that would solve likelihood-free inference problems. We design a recurrent inference machine that learns a sequence of parameter updates leading to good parameter estimates, without ever specifying some explicit notion of divergence between the simulated data and the real data distributions. We demonstrate our approach on toy simulators, showing promising results both in terms of performance and robustness.