Although exact descriptions of the quantum mechanics of molecules are computationally intractable, chemists and physicists have devised approximations that are efficient enough to be practical and accurate enough to be useful.
In an IBM lab in Yorktown Heights, N.Y., a circuit board sits at the bottom of a large tub cooled to temperatures colder than those of outer space. Shiny, solderlike zigzags of niobium cover the board, connecting 16 unusual computing elements. These elements, called quantum bits, or qubits, may form the basis of future computers that will solve problems by taking advantage of quantum mechanics. So far, quantum computers like IBM’s 16-qubit system can solve only simple problems, all of them easy enough to be handled by traditional computers. This spring, IBM set a quantum-computing record by modeling beryllium hydride—which contains a mere three atoms (Nature 2017, DOI: 10.1038/nature23879). Earlier prototypes modeled hydrogen and factored the number 15. As quantum computers become more sophisticated, they will allow chemists to solve problems that are intractable on today’s desktops and even supercomputers. In fact, physicists expect that chemistry simulations will be quantum
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.
Quantum chemistry focuses on modelling and simulating the behaviour of molecular systems using the fundamental principles of quantum mechanics. However, the underlying equations, such as the Schrödinger equation for computing the ground state of N electrons, which is a partial differential equation defined on R3N, suffer from the curse of dimensionality. As a result, simulating even moderately sized molecules demands advanced techniques in analysis, approximation and reduced-order modelling for overcoming the naive computational complexity. In this workshop, the rapidly growing mathematical community working in the field together with several quantum chemists and physicists were gathered to discuss recent advances in areas such as (1) the mathematical and numerical analysis of standard models used in the field, including Density Functional Theory, Coupled Cluster, and the Density Matrix Renormalization Group (2) the development of efficient numerical methods, relying e.g. on the development of error bounds and (3) the opportunities of recent data-driven methods towards the approximation of wavefunctions or density matrices.