Computational complexity in quantum chemistry

Yudong Cao, Jonathan Romero, Jonathan P. Olson +10 more

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

James Daniel Whitfield, Peter J. Love, Alán Aspuru‐Guzik

In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere shortcomings of the algorithm designers and programmers but could stem from the inherent difficulty of simulating quantum systems. Extensions of computer science and information processing exploiting quantum mechanics has led to new ways of understanding the ultimate limitations of computational power. Interestingly, this perspective helps us understand widely used model chemistries in a new light. In this article, the fundamentals of computational complexity will be reviewed and motivated from the vantage point of chemistry. Then recent results from the computational complexity literature regarding common model chemistries including Hartree-Fock and density functional theory are discussed.

BuhmSoon Park

Yasuaki Ito, Satoki Tsuji, Haruto Fujii +4 more

Computational quantum chemistry is a theoretical approach that utilizes the principles of quantum mechanics to perform computations on the electronic structure of molecules and atoms. This method enables the prediction of properties such as molecular structure, energy, electron orbitals, and electron density. In the field of the first principles, or ab initio, which relies solely on computation and not on experimental data, mathematical understanding allows even those without a background in chemistry to perform molecular orbital computations. The computation of quantum chemistry is computationally intensive, making them highly applicable in the field of high-performance computing. However, initiating quantum chemistry can be challenging for newcomers due to the numerous specialized terms and complex equations from quantum mechanics and chemistry. Therefore, this paper aims to provide a clear and accessible compilation of the fundamental and essential algorithm of the Hartree- Fock method, from theory to implementation. The goal is to offer the minimum required knowledge, in an approachable manner, serving as a starting point for those interested in computational quantum chemistry.

Vasileios Armaos, Dimitrios A. Badounas, Paraskevas Deligiannis +1 more