Antoine Brillant, Peter Groszkowski, et al.
Physical Review Letters
Parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parametrized quantum circuits in the limit of a large number of qubits and variational parameters. Then, we find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. Finally, we validate our analytic results with numerical experiments.
Antoine Brillant, Peter Groszkowski, et al.
Physical Review Letters
Alexander Miessen, Daniel J. Egger, et al.
PRX Quantum
Stefano Mensa, Emre Sahin, et al.
Machine Learning: Science and Tech.
Aleksandros Sobczyk
ACS Spring 2024