Quantum Computing for Computational Sciences

Abstract

This article presents a comprehensive survey of the current frontier in quantum computing for computational sciences, evaluating the technical requirements to translate theoretical asymptotic speedups into practical utility in the areas of chemistry, biochemistry, and materials science. We review foundational algorithms, including the quantum Fourier transform, quantum phase estimation, and the quantum linear-system solver, along with variational heuristics such as variational quantum eigensolver and quantum approximate optimization algorithm. Particular emphasis is placed on near-optimal Hamiltonian simulation frameworks, specifically qubitization and quantum signal processing. Furthermore, we shed light on the current advances in quantum error correction codes, quantum hardware, and quantum software platforms. We then provide a comprehensive review of the application of quantum algorithms in four computational science domains that collectively represent the most compelling near-term targets for quantum advantage. This article aims to provide a clear and balanced perspective on the current state of the field and its future potential for advancing computational science.