Fast suppression of classification error in variational quantum circuits

TL;DR

This paper demonstrates that extensive variational quantum circuits with optimal classical post-processing can exponentially reduce classification error, approaching the Helstrom limit, unlike non-extensive architectures.

Contribution

It introduces an optimal classical post-processing method for VQCs and analyzes how circuit architecture affects error suppression and ultimate discrimination limits.

Findings

Error decays exponentially with circuit depth in extensive VQCs

Non-extensive VQCs like quantum CNNs are sub-optimal

Symmetry utilization improves VQC performance

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. 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.