Stochastic Gradient Line Bayesian Optimization: Reducing Measurement Shots in Variational Quantum Algorithms

Optimization of parameterized quantum circuits is indispensable for the application of near-term quantum devices to computational tasks using variational quantum algorithms (VQAs). However, existing optimization algorithms require an excessive number of quantum measurement shots, and their cost is a critical obstacle for practical use. In this work, we propose an efficient framework, stochastic gradient line Bayesian optimization (SGLBO), for circuit optimization in VQAs with fewer measurement shots. The key idea of SGLBO is to estimate the appropriate update direction of parameters based on stochastic gradient descent (SGD), and further utilize Bayesian optimization (BO) to estimate the optimal step size at each iteration in SGD. We combined this idea with an adaptive measurement shot strategy and suffix averaging techniques to achieve efficient optimization while reducing the effects of statistical and hardware noise. Numerical simulations show that SGLBO augmented with these techniques can significantly reduce the required number of measurement shots and the robustness against hardware noise compared to other state-of-the-art optimizers in representative tasks of VQAs.