Adaptive Observation Cost Control for Variational Quantum Eigensolvers

The objective to be minimized in the variational quantum eigensolver (VQE) has a restricted form, which allows a specialized sequential minimal optimization (SMO) that requires only a few observations in each iteration. However, the SMO iteration is still costly due to the observation noise -- one observation at a point typically requires averaging over hundreds to thousands of repeated quantum measurement shots for achieving a reasonable noise level. In this paper, we propose an adaptive cost control method, named subspace in confident region (SubsCoRe), for SMO. SubsCoRe uses the Gaussian process (GP) surrogate, and requires it to have low uncertainty over the subspace being updated, so that optimization in each iteration is performed with guaranteed accuracy. The adaptive cost control is performed by first setting the required accuracy according to the progress of the optimization, and then choosing the minimum number of measurement shots and their distribution such that the required accuracy is satisfied. We demonstrate that SubsCoRe significantly improves the efficiency of SMO, and outperforms the state-of-the-art methods.

Flow-based Sampling for Entanglement Entropy and the Machine Learning of Defects

We introduce a novel technique to numerically calculate R\'enyi entanglement entropies in lattice quantum field theory using generative models. We describe how flow-based approaches can be combined with the replica trick using a custom neural-network architecture around a lattice defect connecting two replicas. Numerical tests for the $\phi^4$ scalar field theory in two and three dimensions demonstrate that our technique outperforms state-of-the-art Monte Carlo calculations, and exhibit a promising scaling with the defect size.

Physics-Informed Bayesian Optimization of Variational Quantum Circuits

In this paper, we propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a VQE-kernel which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty. Moreover, we propose a novel acquisition function for Bayesian optimization called Expected Maximum Improvement over Confident Regions (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly ``observed''. As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.