Designing shallow-depth quantum classifiers with a variational Monte Carlo framework

Variational quantum algorithms (VQAs) serve as a powerful platform for solving machine learning problems on noisy quantum devices. Despite its potential, such method faces severe challenges when applied to large and complex datasets due to the barren plateau problem caused by the fast vanishing gradient, which limits the VQAs’ performance. To overcome this, we propose a low-depth quantum neural network design with the help of variational quantum Monte Carlo method. Our approach leverages a group of shallow variational quantum circuits to increase the overall performance by optimizing the distribution function of a family of random circuits. Specifically, we introduce a hybrid end-to-end encoding method to better represent the dataset features and employ trainable distribution functions to sample the parameters of the hybrid classifiers, enabling improved flexibility and adaptability to capture intricate data patterns. By iteratively optimizing the expected value of the variational wave function over a distribution of sampled circuits, we achieve a robust and effective learning process. Numerical simulations further demonstrate the potential of our method of using shallow quantum circuits to solve classical and quantum classification problems.