Adaptive shot allocation for fast convergence in variational quantum algorithms
This work addresses the optimization bottleneck in VQAs for applications like chemistry and materials science, representing an incremental improvement over prior methods.
The paper tackles the challenge of efficient classical optimization for Variational Quantum Algorithms (VQAs) by introducing a new stochastic gradient descent method with adaptive shot allocation, called gCANS, which reduces both the number of iterations and shots required, thereby lowering time and cost for running VQAs on cloud platforms.
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.