Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers
This work addresses a key bottleneck in variational quantum algorithms for quantum computing researchers, offering incremental improvements in optimization efficiency.
The paper tackles the problem of efficient gradient estimation in variational quantum eigensolvers by proposing a Bayesian parameter shift rule that uses Gaussian processes for flexible gradient estimation with uncertainty information, and numerical experiments show it significantly accelerates stochastic gradient descent and outperforms state-of-the-art methods like sequential minimal optimization.
Parameter shift rules (PSRs) are key techniques for efficient gradient estimation in variational quantum eigensolvers (VQEs). In this paper, we propose its Bayesian variant, where Gaussian processes with appropriate kernels are used to estimate the gradient of the VQE objective. Our Bayesian PSR offers flexible gradient estimation from observations at arbitrary locations with uncertainty information and reduces to the generalized PSR in special cases. In stochastic gradient descent (SGD), the flexibility of Bayesian PSR allows the reuse of observations in previous steps, which accelerates the optimization process. Furthermore, the accessibility to the posterior uncertainty, along with our proposed notion of gradient confident region (GradCoRe), enables us to minimize the observation costs in each SGD step. Our numerical experiments show that the VQE optimization with Bayesian PSR and GradCoRe significantly accelerates SGD and outperforms the state-of-the-art methods, including sequential minimal optimization.