Fast decay of classification error in variational quantum circuits

Abstract

Variational quantum circuits (VQCs) have shown great potential in near-term applications. However, the discriminative power of a VQC, in connection to its circuit architecture and depth, is not understood. To unleash the genuine discriminative power of a VQC, we propose a VQC system with the optimal classical post-processing---maximum-likelihood estimation on measuring all VQC output qubits. Via extensive numerical simulations, we find that the error of VQC quantum data classification typically decay exponentially with the circuit depth, when the VQC architecture is extensive---the number of gates does not shrink with the circuit depth. This fast error suppression ends at the saturation towards the ultimate Helstrom limit of quantum state discrimination. On the other hand, non-extensive VQCs such as quantum convolutional neural networks are sub-optimal and fail to achieve the Helstrom limit, demonstrating a trade-off between ansatz complexity and classification performance in general. To achieve the best performance for a given VQC, the optimal classical post-processing is crucial even for a binary classification problem. To simplify VQCs for near-term implementations, we find that utilizing the symmetry of the input properly can improve the performance, while oversimplification can lead to degradation.

Application of Quantum Recurrent Neural Network in Low-Resource Language Text Classification

“…For a fair comparison, the depth of the VQC in the traditional QRNN was set to 2. Reference [38] mentions that when the architecture of the VQC is extensive when the circuit depth does not decrease the number of gates -the quantum data classification errors of VQC typically decrease exponentially with the increase in circuit depth. This rapid error suppression ends when reaching the final Helstrom limit of quantum state discrimination.…”