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.

Department of Chemistry and Chemical Biology Harvard University Cambridge Massachusetts 02138 United States Department of Chemistry University of Toronto Toronto Ontario M5G 1Z8 Canada Department of Computer Science University of Toronto Toronto Ontario M5G 1Z8 Canada

Department of Chemistry and Chemical Biology Harvard University Cambridge Massachusetts 02138 United States Department of Physics Harvard University Cambridge Massachusetts 02138 United States

Department of Chemistry and Chemical Biology Harvard University Cambridge Massachusetts 02138 United States Zapata Computing Inc Cambridge Massachusetts 02139 United States

Department of Chemistry and Chemical Biology Harvard University Cambridge Massachusetts 02138 United States Zapata Computing Inc Cambridge Massachusetts 02139 United States Department of Chemistry University of Toronto Toronto Ontario M5G 1Z8 Canada Department of Computer Science University of Toronto Toronto Ontario M5G 1Z8 Canada Canadian Institute for Advanced Research Toronto Ontario M5G 1Z8 Canada Vector Institute for Artificial Intelligence Toronto Ontario M5S 1M1 Canada

Department of Physics Harvard University Cambridge Massachusetts 02138 United States Research Laboratory of Electronics Massachusetts Institute of Technology Cambridge Massachusetts 02139 United States Department of Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 United States

Intel Laboratories Intel Corporation Santa Clara California 95054 United States

J Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic v v i Doleǰskova 3 18223 Prague 8 Czech Republic

Zapata Computing Inc Cambridge Massachusetts 02139 United States

Zapata Computing Inc Cambridge Massachusetts 02139 United States Department of Physics and Astronomy Macquarie University Sydney NSW 2109 Australia Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada

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