Error Analysis of the Variational Quantum Eigensolver Algorithm

TL;DR

This paper investigates the robustness of the Variational Quantum Eigensolver (VQE) in noisy quantum environments, revealing that even single errors can cause collapse, impacting the feasibility of near-term quantum algorithms without error correction.

Contribution

It provides a comprehensive error analysis of VQE, demonstrating its vulnerability to noise and highlighting the challenges for near-term quantum computing applications.

Findings

VQE collapses with single errors during quantum calls

Error sensitivity of VQE affects near-term quantum algorithms

Implications for resource-efficient quantum computing without error correction

Abstract

Variational quantum algorithms have been one of the most intensively studied applications for near-term quantum computing applications. The noisy intermediate-scale quantum (NISQ) regime, where small enough algorithms can be run successfully on noisy quantum computers expected during the next 5 years, is driving both a large amount of research work and a significant amount of private sector funding. Therefore, it is important to understand whether variational algorithms are effective at successfully converging to the correct answer in presence of noise. We perform a comprehensive study of the variational quantum eigensolver (VQE) and its individual quantum subroutines. Building on asymptotic bounds, we show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call. We discuss the significant implications of this result in the context of being able to run any variational type algorithm without resource expensive error correction protocols.