Can Variational Quantum Algorithms Demonstrate Quantum Advantages? Time Really Matters

Understand

Applying low-depth quantum neural networks (QNNs), variational quantum algorithms (VQAs) are both promising and challenging in the noisy intermediate-scale quantum (NISQ) era: Despite its remarkable progress, criticisms on the efficiency and feasibility issues never stopped.

• However, whether VQAs can demonstrate quantum advantages is still undetermined till now, which will be investigated in this paper.
• First, we will prove that there exists a dependency between the parameter number and the gradient-evaluation cost when training QNNs.
• Noticing there is no such direct dependency when training classical neural networks with the backpropagation algorithm, we argue that such a dependency limits the scalability of VQAs.