Variational Quantum Algorithm Landscape Reconstruction by Low-Rank Tensor Completion

TL;DR

This paper introduces a low-rank tensor completion method to efficiently reconstruct high-resolution cost function landscapes in variational quantum algorithms, aiding their development and analysis.

Contribution

The paper proposes a novel low-rank tensor completion approach to reconstruct VQA landscapes, reducing the need for extensive cost function evaluations.

Findings

Effective reconstruction of high-dimensional landscapes

Application to penalty term analysis in constrained optimization

Examination of probability landscapes of basis states

Abstract

Variational quantum algorithms (VQAs) are a broad class of algorithms with many applications in science and industry. Applying a VQA to a problem involves optimizing a parameterized quantum circuit by maximizing or minimizing a cost function. A particular challenge associated with VQAs is understanding the properties of associated cost functions. Having the landscapes of VQA cost functions can greatly assist in developing and testing new variational quantum algorithms, but they are extremely expensive to compute. Reconstructing the landscape of a VQA using existing techniques requires a large number of cost function evaluations, especially when the dimension or the resolution of the landscape is high. To address this challenge, we propose a low-rank tensor-completion-based approach for local landscape reconstruction. By leveraging compact low-rank representations of tensors, our technique can overcome the curse of dimensionality and handle high-resolution landscapes. We demonstrate the power of landscapes in VQA development by showcasing practical applications of analyzing penalty terms for constrained optimization problems and examining the probability landscapes of certain basis states.