Adaptive Observation Cost Control for Variational Quantum Eigensolvers

2025-02-03

AI Summary

To address the high observational cost of Sequential Minimal Optimization (SMO) in Variational Quantum Eigensolvers (VQEs) caused by quantum measurement noise, this paper proposes SubsCoRe—an adaptive observational resource allocation method. SubsCoRe introduces a novel confidence-subspace-based mechanism that dynamically adjusts both shot count and shot distribution: leveraging a Gaussian Process (GP) surrogate model, it identifies low-uncertainty subspaces in real time during optimization and allocates measurement resources adaptively—thereby ensuring reliable parameter updates while reducing per-iteration observational overhead. Experimental results demonstrate that SubsCoRe significantly reduces the total number of measurements required by VQE-SMO while preserving ground-state energy accuracy. It achieves superior observational efficiency compared to state-of-the-art methods, with controllable accuracy and strong robustness against noise.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

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.

Problem

• Reduces observation noise in VQE
• Optimizes measurement shots distribution
• Improves SMO iteration efficiency

Innovation

• Adaptive cost control method
• Gaussian process surrogate
• Minimum measurement shots distribution