  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.
