  Variational Quantum Algorithms (VQAs) are a promising approach for practical
applications like chemistry and materials science on near-term quantum
computers as they typically reduce quantum resource requirements. However, in
order to implement VQAs, an efficient classical optimization strategy is
required. Here we present a new stochastic gradient descent method using an
adaptive number of shots at each step, called the global Coupled Adaptive
Number of Shots (gCANS) method, which improves on prior art in both the number
of iterations as well as the number of shots required. These improvements
reduce both the time and money required to run VQAs on current cloud platforms.
We analytically prove that in a convex setting gCANS achieves geometric
convergence to the optimum. Further, we numerically investigate the performance
of gCANS on some chemical configuration problems. We also consider finding the
ground state for an Ising model with different numbers of spins to examine the
scaling of the method. We find that for these problems, gCANS compares
favorably to all of the other optimizers we consider.
