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Quantum Information Processing

Variational quantum algorithms: fundamental concepts, applications and challenges

Han Qi, Sihui Xiao, Zhuo Liu, Changqing Gong, Abdullah Gani

Published Jun 3, 2024• 37 citations
Publisher
DOI
10.1007/s11128-024-04438-2

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Abstract Quantum computing in the noisy intermediate-scale quantum (NISQ) era has foregrounded the importance of Variational Quantum algorithms (VQAs). These algorithms are crucial for addressing complex quantum mechanical problems that challenge classical computers. One such problem is the electron-phonon (e-ph) interaction, which is essential for determining the zero-point renormalization (ZPR) of electronic structure properties. The calculation of ZPR of fundamental gap relies on the accurate computation of ionization potential (IP) and electron affinity (EA) energy levels in molecular systems, where the VQAs offer the promising solutions. Despite the critical importance of IP, EA energies and ZPR in quantum chemistry calculations, research into the application of quantum algorithms for these calculations remains limited. To address these challenges, we propose two quantum algorithms for ZPR of fundamental gap calculation using Variational Quantum Deflation (VQD) and Quantum equation of Motion (QEOM) algorithm for several molecular systems. This work opens up new possibilities for the accurate and efficient study of e-ph interaction in electronic structure calculations, even with NISQ-era hardware.
Variational quantum algorithms (VQAs) constitute a prominent paradigm for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum Architecture Search (QAS) has emerged as a critical research area to automate the discovery of high-performing circuit structures. This paper reviews key advancements in current research on QAS, including its core concepts, representative methodologies, applications, and emerging trends. The content is structured to ensure broad accessibility for a diverse audience of researchers while preserving the core principles of complex methodologies. In addition, we discuss remaining challenges and suggest potential research directions to offer perspectives on future exploration in this rapidly evolving field.