EAGER‐QAC‐QSA: Quantum Chemistry with Mean-field Cost from Semidefinite Programming on Quantum Computing Devices

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David A. Mazziotti of The University of Chicago is supported by an award from the Chemical Theory, Models and Computational Methods program in the Division of Chemistry and the Condensed Matter and Materials Theory program in the Division of Materials Research to harness the potential of quantum computing to study problems in chemistry and materials science. The proposal was submitted in response to the Quantum Algorithm Challenge Dear Colleague Letter, NSF 20-056. Many new molecules and materials that are critically important to improving society are so complex that they are difficult to study on conventional computers. Mazziotti and his research group are pursuing novel quantum chemistry algorithms that exploit the advantages of quantum computers to predict the energies and other properties of molecules and materials at a much lower computational cost. The work has the potential to be transformative in that it aims to enable applications to much larger molecules with larger numbers of electrons, opening new vistas for quantum computing in chemistry and materials. Mazziotti and his group are also driving educational and outreach activities including a quantum computing curricula for chemistry at the University of Chicago as well as an interactive Zoom classroom series for teaching quantum chemistry, information, and computing to undergraduate and high school students beyond the University of Chicago.Even though remarkable strides have been made in hardware and algorithms, a quantum advantage of quantum computers over classical computers has not been demonstrated in molecular simulations. Noise on current and near-term devices has limited the sizes of the molecules and the numbers of electrons that are treatable to below the classical limit. Mazziotti and his research group are pursuing a new paradigm for quantum computing in which the two-electron reduced density matrix (2-RDM) is computed directly on the quantum computer. This approach represents a dramatic departure from all existing algorithms that prepare the wave function and subsequently perform measurements of target observables. Direct preparation of the 2-RDM, constrained by suitable conditions to enforce its representation of at least one N-electron density matrix, does not encounter the traditional bottlenecks of wave function simulations such as deep circuits or non-trivial high-dimensional classical optimization. Specifically, we propose a quantum semidefinite programming (SDP) algorithm for the direct variational computation of the 2-RDM on quantum computers. The quantum solution of semidefinite programs has the potential to reduce the computational cost of treating strong electron correlation to that of a mean-field calculation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.